The Black Cats headed into a home date with their fiercest rivals without a win in their opening eight fixtures and having already switched managers from Paolo Di Canio to Poyet.
It was, however, to be an afternoon to remember for the Wearside natives, with Fabio Borini stepping off the bench to net a stunning winner in a 2-1 success.
Poyet, who was taking charge of Sunderland for just the second time, was left beaming at the final whistle as he paid tribute to the efforts of those he sent into battle.
He told Sky Sports: "I think everything is big today. It was the first win, which is key - you need to start winning football games - against our biggest rivals, in my first home game, somehow.
"Sometimes it's not about playing well in these games, it's about winning.
"I'm sure that, at least for the next few days, the fans are going to be delighted and the players are going to be relieved."
Poyet stopped short of replicating the famous celebration of his predecessor during a victory at St James' Park back in April, but savoured the moment just as much as he collected his first points as a Premier League boss.
He added: "I did enjoy it. When I saw the four minutes of extra-time I nearly had a heart attack, but that's the way it is at the moment for us - nothing is going to be easy.
"Everything is about effort and we put players on the pitch who gave everything.
"Then there was a moment when we needed to take a risk, go for the game, and what a goal to win the game, what a time to score - everything was spot on."