Poyet following the footsteps of his predecessor Pablo Di Canio beat rivals Newcastle in his early days as manager of struggling Suderland.
Fabio Borini helped Sunderland to a 2-1 win over Newcastle United in the Wear-Tyne derby and their first three-point haul of the season.
Gus Poyet, in just his second game in charge of the Black Cats, saw Steven Fletcher break the deadlock at the Stadium of Light, only for Mathieu Debuchy's first goal in English football to restore parity.
There was, however, to be a late twist in the tale as Borini stepped off the bench to offer renewed optimism in what has been a forgettable campaign on Wearside.
It took just five minutes for the hosts to break the deadlock, with Fletcher rising above Newcastle youngster Paul Dummett - making his first top flight start - to nod home an Adam Johnson delivery.
The Magpies levelled matters just before the hour mark, with a cross-shot from Hatem Ben Arfa allowed to run through to the back post for Debuchy to bundle past Keiren Westwood from close range.
Borini was introduced in place of Johnson as Poyet went looking for a winner, and the on-loan Italian duly obliged as he gathered a pass from Jozy Altidore and cracked a 20-yard drive high into the top corner.
It was a match Sunderland simply could not afford to lose for a variety of reasons and they went about their task with some relish.
The absence of a recognised centre-half pairing for the Magpies - neither Fabricio Coloccini or Steven Taylor was able to plug the gap left by the suspended Mapou Yanga-Mbiwa, placing the onus on specialist left-back Paul Dummett - gave the Black Cats an opportunity, and it was one they were to exploit within minutes.
Johnson played a corner short to Sebastian Larsson and then delivered the return pass to the far post for Fletcher to climb high above Dummett and head home.
It was the perfect start to Poyet's first game at the Stadium of Light and for 20 heady minutes or more, Sunderland dominated proceedings with Lee Cattermole leading the fight from central midfield and his team-mates following suit.
Magpies boss Alan Pardew, who had started as he did against Liverpool last week with Ben Arfa at the pinnacle of 4-2-3-1 formation, was forced to abandon Plan A with his team simply not competing, and with Loic Remy moved into an advanced position and the former Marseille man dropping deeper, Newcastle were far more effective.
However, all their better attempts came from distance with Yohan Cabaye prompting Westwood to make his only real first-half save with a dipping 16th-minute free kick, but both he and Ben Arfa were significantly more wayward thereafter.
Perhaps the Magpies' most promising attack of the opening 45 minutes came eight minutes before the break when left-back Davide Santon picked out right-back Debuchy with an elegant pass and Larsson had to head his dangerous cross away with black and white shirts arriving in numbers.
Pardew opted for further change at the break, sending on striker Papiss Cisse for midfielder Moussa Sissoko, but the Magpies were able to create little during the opening exchanges of the second half despite enjoying a wealth of possession.
But they were back in it 12 minutes after the restart when Ben Arfa, who had been infuriatingly ineffective until that point, accepted Cabaye's pass and drove a low cross across the face of goal for Debuchy to convert at the far post.
However, Borini almost made his name on Wearside within seconds of his arrival as a 69th-minute replacement for Johnson, blasting a shot through Krul, only to see the Dutchman gratefully grab the ball at the second attempt.
Santon drilled a skidding effort just wide with 14 minutes remaining and derby specialist Shola Ameobi, on as a 70th-minute replacement for Remy, went just as close two minutes later.
But the decisive moment came five minutes from time when Borini ran on to Altidore's lay-off and smashed an unstoppable shot past Krul to win it.
Sunderland manager Poyet will no doubt be hoping this victory today will kick start their march away from the relegation zone. Will this become a reality? Only time will tell.
Sunderland: Westwood, Bardsley (Celustka 77), O'Shea, Cuellar, Dossena, Larsson, Cattermole (Ki 70), Colback, Johnson (Borini 69), Altidore, Fletcher
Substitutes not used: Gardner, Giaccherini, Mannone, Roberge