72 Hours has Damien systematically annihilate the cheerleaders (the Brat Pack) by exploiting their mutual distrust for one another. By breaking into their compound and escaping unseen, he's easily able to cause the simmering tension in the group to boil over. Within a couple of hours, every one of them is dead, and they've even disposed of his redundant lackey for him in the process.
In the Calvin At Camp episode "Jason Fox The Musical," Eugene tricks the Eds into recruiting kids to help them with scams. Once there is no one to scam, he assumes that the kids will turn on each other in frustration.
In Kyon Big Damn Hero, when Kyon, Koizumi, Yuki and Mikuru go to see the Student Council President:
Kyon: Haruhi's going to burst into the middle of the meeting and be really pissed off about not being involved.
Koizumi: Ah... You're certain?
Kyon: She absolutely will if you send a text to her just before we enter the Student Council room. That should give Kimidori-san enough time to state her goals and reasons, but not to actually do anything before Haruhi shows up.
In Mass Foundations: Redemption in the Stars, The Courier and others only manage to escape from the Alingon base by trusting the asari guard they spared earlier. She returned the favour by creating the inpenetrable biotic barrier in front of the Shadow Broker's group and preventing them from attacking.
The whole story starts with Phoenix accidentally getting summoned to Equestria by Twilight after several failed attempts at finding a lawyer to defend her friend. As the story progresses is revealed that Phoenix was summoned intentionally by Twilight, following Princess Celestia's advice, who knows about the titular ace attorney and made her summon him in full confidence that, notwithstanding getting dragged into a completely alien world to him, he would never turn his back on an innocent being accused of a crime.
In A Charmed Life Light's final plan in his game with L hinges on the fact that he, the Chief's son, is well-liked and trusted by the police whereas L, an outsider who is poking into their affairs and casually disregards the feelings of his alleged allies, is not.
Forward has a couple of these, the first being one hatched by River and Jayne while being held captive by Niska, which allows them to break free by convincing Niska to kill one of his goons and Jayne palming a weapon from his body. Later on, River uses one to convince the rest of the crew that she's dangerously unstable, so they leave her behind while going on a job, during which she is able to sneak away and do a job on the side.
In Order of the Dragon Ron makes a plan which depends heavily on Percy's estrangement from his family and brown-nosing of Cornelius Fudge.
In Princess Of The Blacks when Jen Black (This universe's Harry Potter) makes a bunch of random trinkets that she claims are wandless foci to conceal that she is proficient at wandless magic. When she hands them over to Dumbledore to inspect she's counting on the fact that the Leader of the Light would sooner destroy powerful artifacts than allow them to remain in the hands of a dark witch. Dumbledore does exactly that destroying the artifacts and the evidence they were just mundane trinkets along with them. Jen then goes on to demand reparation from him for destroying her "family heirlooms."
Queen Of All Oni: Uncle knows that Daolon Wong knows how to summon Tarakudo, who the heroes need to interrogate for information on Jade, and also that he won't divulge it willingly. So, with help from Captain Black, Uncle stages a jailbreak, convincing Wong that he's gone behind the backs of the other heroes, so Wong will help him conjure Tarakudo. When the ritual is successful, Wong predictably double crosses Uncle and tries to cut a deal with Tarakudo — at which point Tohru and the Section 13 agents waiting outside the shack they're in bust in, arresting Wong and leaving Uncle and Tohru to question Tarakudo.
In an example that crosses over with Indy Ploy, due to coming up with it on the spot: when Jade attacks the shop in order to capture Tohru for Ikazuki, Uncle has him wait inside the shop's protective wards. In order to get him to come out, Jade has her ninja perform a sneak attack on Uncle, knowing Tohru will come to his aid, leaving himself to be captured.
Operation Steel Lightning is basically one big one of these: Jade plans on letting the newest mask "accidentally" end up on one of the good guys (it was meant to be Jackie, but ends up on Captain Black instead), forcing them to tap into its powers (which she accomplishes by tossing Black off a tower), hitching a ride into Section 13 in their shadow (with the mask's awakened powers hiding her presence from Uncle's protective wards), then using a spell to fully awaken the General inside and having them distract the agency while she breaks into the Vault and steals the other masks and the Talismans. And it almost goes off without a hitch, with only Agent Wisker's unforeseen interference preventing a victory. BUT, Jade still gets away with the info the heroes had on the Teachings (a Shadowkhan/Oni Tome of Eldritch Lore) as a Consolation Prize.
The Villain Protagonist Tyrin Lieph in The Council Era successfully predicts exactly how the Council will respond to his son's death, how the dezba will respond to a dezban high chieftain's execution, and how the public will respond to the dezba's reaction in order to massacre the dezba, who he perceives to be a threat to galactic security.
A Future of Friendship, A History of Hate: Fury Cross leaves a wrath wound on Rainbow Dash in their first fight, then pisses her off during their rematch; the wrath wound feeds on her anger and weakens her, allowing him to curbstomp her. Fortunately, her friends show up in time to save her and help beat him.
He also deliberately mentions where his encampment is in relation to Ghastly Gorge (the battleground chosen for their rematch), knowing Rainbow Dash will deduce it and meet him there alone, while her friends go to the Gorge.
Miserain gives Scootaloo the Tear of Covet, knowing that her wish will backfire and leave her miserable, feeding and releasing the woebeghoul contained within.
In Neon Exodus Evangelion, Lucifer (also known as Unit 01) absorbs DJ after the final battle in the series, then stays passive afterward so he can be piloted by one of Natlateth's cloned pilots. Asuka almost screws this up by breaking into the SEELE-controlled Geofront and starting Lucifer up to try and talk to DJ, but manages to avoid it by taking over his body directly and piloting him like a production-model Eva. The culmination of the plan is DJ taking over in the middle of the final combat, so Natlateth stabs Lucifer with the Lance of Longinus. Since DJ is Longinus, and Lucifer became Unit 01 after sustaining wounds by the same Lance while trying to redeem himself, the outcome is that the Redemption is finished. If Natlateth hadn't thought Lucifer was truly dead and had left him at the Geofront, the plan would have failed.
In Futari Wa Pretty Cure Blue Moon, Kainatrol likes to do this when she isn't outright using Mind Control. In one mini-arc, she starts one up by controlling Mia and using her to lure Asa and Yoko to one roof so that Tachimany can ambush them, which they do, leaving the Cures badly beaten. Kainatrol is then outsmarted by Dawn's own Batman Gambit, though, relying on Kainatrol's sadism and her tendency to go Drunk on the Dark Side when she's getting her way (or blow up if she's not). She hands over a fake Moon Piece, slipping Mia the real one to break the mind control and letting Kainatrol jump on the chance to mind-control Dawn/Kirei herself. This also buys time for Asa and Yoko when Ami shows up and Kainatrol can't resist making the two of them fight each other instead.
In With Strings Attached, the four manage to prevail thanks to a series of Batman Gambits that take advantage of the desperation and boredom of the skahs and the paranoia of the Raleka, as well as Brox's overconfidence.
Hokuto's plan to use Kuyou as a distraction while he steals the Artifact of Doom he needs for his plans from Yokai Academy's archives hinged solely on exploiting Kuyou's desire for revenge on Tsukune. It works like a charm.
In chapter 13, with the revelation that Tsukune's Holy Lock is cracking, Dark claims that he's only keeping Tsukune alive so that Kokoa can atone for her actions and regain her vampire pride, after which he'll kill him to prevent the ghoul from surfacing. However, as Mizore and Felucia explain, if Dark hadn't mentioned Kokoa's debt to Tsukune and act like it was still safe, the headmaster would have had Tsukune killed, knowing that Dark would be the first to kill Tsukune if the ghoul posed any threat; in doing so, Dark has bought the group time to find a way to repair the lock.
In Survivor: Fan Characters, Vinnie from Season 2 and 6 is exceptionally well-known for pulling these off, often getting his enemies voted off easily without fail. From Season 5, Gatemaster is also adept at these, although his relies on luck a lot more, and he uses one to get the final four he wants.
Subverted in the case of Phil from Season 7: he tries to pull one off a la Richard Hatch from Survivor: Borneo, when he quits the final immunity challenge on the assumption that whoever won would take him to the finals with them, and it fails spectacularly when Ker votes him off and takes Wrecker instead.
In the fic By the Fire's Light Detective Carl Rourke and Mira Grolinksy try to use the Slender Man's meta nature against it, so they can curb its destructive nature and save its victims. It ends up failing miserably.