Example of the "Big Bad manipulates the actors to fight and eliminate each other" trope: the miniseries Crisis on Infinite Earths featured a subsidiary story arc involving Brainiac and the Earth-One Lex Luthor assembling an army of supervillains to attack the remaining superheroes. Brainiac and Luthor had led their villain army to believe that the superheroes would be easily defeated owing to the villains outnumbering the heroes (who were already distracted dealing with the huge honkin' crisis that was unfolding in the main story arc); however, the real plan was to have the heroes and the other villains kill each other off so that when the the dust finally cleared, Brainiac and Luthor would be the last superpowered "men" standing, and therefore be able to take over all the remaining universes without anyone left to defeat them. If Whatever Happened to the Man of Tomorrow? is any indication, Brainiac planned to dispose of Luthor soon after.
A blatant example in a Suicide Squad Annual as the Squad are trying to find the near-mythical spy agency known as Argent. They track them down to a college only to find a base packed with agents of the terrorist group Kobra. As it happens, Amanda Waller already figured that Argent (who basically comprise of a half dozen people) specializes in getting groups to take each other out to make their jobs easier. Rick Flagg even lampshades "it's the old 'let's have him and you fight' routine."
In Gotham City Garage, Batman makes Barbara Gordon believe Kara killed their father to turn her against her little sister. His deceit almost works, but Harley tells Barbara the truth before she meets Kara.
In an interesting inversion, Plastic Man #4 has the titular hero spreading himself thin, then standing between two robots, causing them to punch each other through the sheet of his body.
Plastic Man: Hey, hey! Rock 'em Sock 'em robots! Now that's more like it! Let's you and him fight!
Lampshaded in DC One Million: the Batman of the 853rd century, having time-traveled back to the present, attacks Nightwing on sight. When asked why, he explains that he was just being polite; according to his research, "masked lawmen" of this time period always fought the first time they met.
In Action Comics #600, Darkseid tried to use illusions to convince Superman that he was battling his minion Amazing Grace and Wonder Woman that she was fighting Kalibak, when in reality Superman and Wonder Woman were fighting each other. Subverted in that the two heroes saw through the deception almost immediately and staged a mock battle, fighting their way toward Darkseid's throne room. As Superman reminded Darkseid, "We may be mere mortals, but we're not stupid!"
This plays out oddly in another issue of Action Comics, where Superman gets into a fight with Diode the Invincible over a misunderstanding... but while he wasn't a member of the murderous Doomslayers roving the area, Diode was a supervillain. After clearing the air, the aged wash-up decided to help Superman take care of the Doomslayers before retiring peacefully.
In Superman vs. Shazam!, Karmang forces Black Adam and the Sandman Superman to trick Superman and Captain Marvel into fighting each other so they are too busy to figure out and ruin his master plan.
Sandman Superman: If Captain Marvel and Superman were to discover these engines on their worlds, and join forces to destroy them, they might learn that one weakness— and it is for this reason that I and Black Adam have been sent to involve the heroes in battle! Fighting each other, the heroes will be too busy to uncover the true threat to their Earths... In this way, both Earth-One and Earth-S will be annihilated— and neither Superman nor Captain Marvel can do a thing to save them!
Strangers at the Heart's Core: Lesla-Lar subtly influences Gravitron Man and Gravity Lord into hating and attempting to destroy each other using their gravity-manipulating weapons, so Supergirl gets killed when she tries to stop them.
In New Krypton, Reactron kills Supergirl's father, and in Who is Superwoman? his ally Superwoman frames Supergirl's best friend Thara Ak-Var (Flamebird) for her father's murder. In The Hunt for Reactron storyline, both friends come to blows.
In Last Daughter of Krypton, when Supergirl arrives on Earth, Superman introduces himself as Kal-El. She attacks him, thinking that he is a villain pretending to be a Kryptonian because she is unaware that Krypton has been destroyed and thinks that it has only been a short time since she left, and when she left, her cousin Kal-El was a mere baby. She eventually relents after the initial misunderstanding.
World's Finest (1941): Doble subversion in issue #176. A movie star called Ronald Jason wants to pull off his career's best performance before dying, so he poses as an alien called Dur and begs Superman to save him from a hitman called Tiron; later, he poses as an alien law-enforcer called Tiron and asks Batman's help to apprehend a dangerous criminal called Dur, who has fled to Earth and has tricked Superman into aiding him. Batman recruits Supergirl to help him hold Superman back, Superman asks Batgirl's help, and both teams fight each other. However, Superman had figured out Jason's gambit, and his reasons. He warned Batman, and the duo decided to humor him so he died happy. And still, they did not let Supergirl and Batgirl in on the secret, so they fought each other for real.
In his first meeting with the Legion of Super-Heroes, the clone Superboy mistakes them for villains. If you translate the Interlac, Saturn Girl says "This must be the 20th century tradition of fighting then teaming-up I've heard about."
The Lightning Saga: Subverted by having Superman introduce the Legion team when they showed up in the past though Karate Kid had been beaten up as Trident earlier and in fact Star Boy had already been on one of the teams. But then they all had issues with each other later.
Also subverted in a different meeting of Superboy and a Legion team. Turns out the mission team had been pretending to be average citizens and had insinuated themselves into his life beforehand.
The series Birds of Prey once hung a lampshade on the trope with a novice crime fighter who was styling herself as the new Batgirl. Using her teleporting powers she had been watching the heroes for a long time and knew not only that they were good guys, but also their names, secret identities and powers, and when they set up an ambush one evening to try and find out who has been masquerading as Batgirl (Something Barbara Gordon, the original Batgirl, does not take lightly) she could not have been happier. As they are fighting she happily converses with all the participants and explains that after they are done fighting they can all be good friends and teammates, because she had gained the impression that fighting at the first meeting was the traditional thing to do.
Batgirl (2000) has a brief scuffle between Cassandra Cain and Connor Hawke. Connor comes to Gotham on the trail of bow-wielding assassins, only for Cassandra to assume he's one of them. It ends when Cassandra fakes being knocked out so she can eavesdrop on him and Eddie Myers, confirming they're not the killers.
Discussed in an issue of The Flash where he and the Pied Piper almost come to blows while investigating the murders of some homeless people.
Young Boy: This is gonna be neat! Flash: Neat? Pied Piper: Neat?! Boy: Sure. You guys are gonna fight now, right? On account of you really like each other, but a supervillain made you misunderstand so now you gotta fight. So you're gonna fight for about an hour, then realize that you've got a common enemy and be life-long friends. Pretty neat! Flash: ... Boy, do I feel predictable. Piper: Let's cut to the part where we team up, okay?
Hitman (1993): Subverted and Deconstructed in the arc "Who Dares, Wins". The Big Bad of the arc is a bunch of crooked British SAS gunning for Tommy and his crew. Tommy has the idea to swindle the Mafia hitmen who have also been chasing them through the whole arc into attacking the SAS, hoping they will either kill each other or the confusion will allow Tommy and his crew to run away. The SAS takes care of the Mafia within a few seconds and one of Tommy's friends gives him a "This Is Reality" speech about how it's two bunches of people who want Tommy very, very dead and they are going to prioritize killing him over anybody else.
Lampshaded in an issue of Justice League of America in the early nineties. Obsidian and Nuklon are waiting to meet up with the JLA to offer to join the team after its most recent roster overhaul, and Obsidian says, "First, they won't even let us join. 'You were in Infinity, Inc.? Wasn't that some kids' group, like Menudo?' Then there'll be some bizarre misunderstanding, and they'll think we're villains, and there'll be a fight, and..."
Batman: No Man's Land has an amusing aversion. Bane manipulates several of the various Gotham gangs into thinking Two-Face has murdered several of their compatriots. Two of the gangs, the Street Demonz and the Eightballs, run into each other while out for revenge and immediately team up to stage an assault on Two-Face's headquarters. No argument, no tension, no Mexican Standoff, no nothing. Apparently, common street gangs are better at teamwork than most crime fighters in the DCU.
DC One Million: The Batman of the future (no, not thatBatman of the Future) meets modern Nightwing, and fights him. Nightwing asks why, and Batman 1-mil says he's honoring the superhero tradition of fighting before teaming up.
Blue Beetle and Green Lantern Guy Gardner had one when they first met, as his ring detected Jaime's Reach technology as a threat. Also notable for the rematch having been broken up by one fighter's mother.
In an early storyline of Justice League International, Maxwell Lord and his computer ally sicced the League on Metron after framing him for creating a rampaging robot. Their plan went awry when it turned out that Metron and Mister Miracle knew each other as New Gods and were more inclined to talk things out.
Justice League (2011) puts together the Justice League in this fashion. Green Lantern gets a tip about alien technology in Gotham and finds Batman. They only argue before teaming up, but since the only alien they know of is Superman, they head to Metropolis to question him. GL calls in the Flash when that doesn't go so well, and they all whale on each other for a while until the alien tech activates and starts spewing Darkseid's Parademons.
Wonder Woman (1942): The Green Geni manage to manipulate Wonder Woman and the Holliday Girls into fighting the Golden Policewomen by framing themselves as victims and the Golden gals as oppressors. The misunderstanding is helped along by one of the Golden Police's own accusations, but the two groups team up to prevent the Geni from escaping to do more harm once the Geni show their true colors.
Wonder Woman (2006) Gorilla Grodd tricks knights from Gorilla City out to stop poachers into attacking Wonder Woman instead. This gets them exiled but Wonder Woman manages to befriend them and give The knights things to do until they are allowed to return home. Wonder Woman's fight with Power Girl isn't a straight example, as Kara had been brainwashed by The Children of Ares, but is an instance were Diana should have just immediately lassoed Power Girl instead of attempting to talk down the other hero down.
Wonder Woman: The Hiketeia: Thanks in part due the manipulations of the Erinyes, their conflict morals in regards to the situation and Diana's obligations as part of the Hiketeia; Wonder Woman and Batman end up coming to blows twice in the story.
In The Multiversity #1, the Multiversity team and the Retaliators come to blows after a bewildered Thunderer knocks out his Earth-8 counterpart.
Watchmen refers to a fight between the Comedian and Ozymandias when they first bumped into each other. Ozymandias shrugs it off as a common enough misunderstanding in reference to the trope, but given the Comedian's personality (and the fact that Ozymandias was investigating the disappearance of Hooded Justice, whom the Comedian might well have murdered) it likely wasn't an accident. And while Ozymandias trivializes the incident, the severe beating he administers (or has administered) to the Comedian as part of murdering him demonstrates that he probably wasn't sincere.
Defied in Aztek: The Ultimate Man. When Aztek is confronted by an angry Green Lantern out for a fight, he simply swipes Kyle's Ring of Power and then hands it straight back.
Aztek: Good, well, now that we've passed the predictable fight superheroes are obliged to have when they first meet and established the fact that I'm not a villain, maybe we can get down to business here. Friends? Kyle: Ring first, then friends.
Lampshaded in the Doctor Thirteen limited series. At one point, Infectious Lass asks if there's going to be a superhero fight, and then points out that in the 31st century, it's common knowledge that superheroes are supposed to fight each other before teaming up.
Secret Origin: In Sandman's origin story, he and the Crimson Avenger get into a brawl, Wesley thinking Crimson is in cahoots with the Phantom of the Fair (and vice versa). They only stop fighting when Wes takes off Crimson's mask to find it's his friend Lee Travis, and unmasks himself to stop his buddy continuing the fight.
