As a Chelsea player in 2000, Poyet's two goals knocked Newcastle out in the semi-final at Wembley as the Blues went on to lift the trophy.
And 12 years later the Brighton manager masterminded a famous win for his side as Will Buckley's shot, deflected into his own net by Mike Williamson, sent the Magpies packing.
Brighton had already knocked Sunderland out of the Carling Cup this season at their new Amex Stadium, and thanks to Buckley's lung-busting run and shot 15 minutes from time, they secured a North-East double scalp.
Newcastle had not been to Wembley since that Poyet-inspired Chelsea defeat but Magpies boss Alan Pardew, a runner-up as a player and a manager, clearly saw the competition as a realistic chance for some silverware.
He named his strongest available line-up with only skipper Fabricio Coloccini missing after he failed to shake off a groin injury.
But they wasted the few opportunities Brighton afforded them with Leon Best the chief culprit.
Best found himself unmarked 18 yards out early on but his low drive flew narrowly wide.
Best squandered an even better chance in the 12th minute when Shola Ameobi headed the ball back across the Brighton six-yard box to his strike partner, who planted his header wastefully over the top.
At the other end Buckley skipped in between Danny Guthrie and Davide Santon far too easily but could not get his shot away.
Buckley roasted Santon again on the half-hour and this time pulled the ball back towards Craig Mackail-Smith but Magpies keeper Tim Krul managed to gather the ball before the Scotland striker pounced.
Mackail-Smith sensed glory moments later when he was teed up by Ashley Barnes but his attempted 20-yard curler was never going to trouble Krul as it sailed wide.
Toon defender Danny Simpson then almost surprised the hosts with a marauding run into the area but Lewis Dunk bravely blocked his shot and Gordon Greer completed the clearance.
Mackail-Smith had a shot deflected wide by James Perch and Adam El-Abd headed the resulting corner over before half-time.
Newcastle were first to threaten after the break with Ameobi again playing in Best, whose shot was kept out by the legs of home keeper Peter Brezovan, and Guthrie's follow-up shot was deflected over.
Brezovan was in action again from the corner, palming a fierce close-range shot on the turn from Ameobi round the post, and he also kept out a low drive from Yohan Cabaye.
Temperatures were starting to rise on the benches after Simpson was booked for a nasty challenge on Mackail-Smith by the touchline, before Poyet's not entirely-serious reaction to Hatem Ben Arfa falling to the ground clutching his ankle seemed to irritate Pardew.
Then Cabaye appeared to lash out with a stray foot into the head of El-Abd as both players tumbled to the floor.
Krul was called into action for the first time in the second half when he parried Mackail-Smith's near-post shot wide in the 70th minute.
And five minutes later Krul was beaten when Buckley got the piece of luck his barnstorming run probably deserved.
The £1million summer signing from Watford picked up the ball in his own half and charged forward into the Newcastle area before side-stepping Cabaye.
His shot looked to be going wide but it took a huge deflection off Williamson to wrong-foot Krul and bounce into the net.
Newcastle had a late penalty shout when Cabaye's shot hit Barnes' arm but the Seagulls survived to reach the last 16 for the second successive year.