The Wearsiders came into the weekend without a win in the league, but a brace from Stephen Fletcher proved crucial for Poyet's men after Connor Wickham's early opener was cancelled out by Charlie Adam.
An inability to score goals had seen Sunderland draw five of their previous six games, but their attacking talent finally clicked at the Stadium of Light, to lift them up to 11th in the league.
Poyet said: "It's a good feeling. I'm very pleased for the players.
"We knew inside the camp that we were a difficult team to play against, but without a win there's always some doubts and some nerves, so I think it was very important for the players to win this game.
"I'm very pleased for Fletcher because I know hard it was for him to be in the situation where a few weeks ago I left him out of the squad.
"He wasn't happy but he took it professionally and kept working. The previous week when we played Swansea we were able to see something special in him. He was getting back to his best in training and he had a chance to score and this week he was outstanding."
The fine form of Wickham and Fletcher in tandem left Poyet in no doubt the duo can play a crucial role in Sunderland's season.
"I thought he [Wickham] was very good up front as a striker but to put Fletcher into the shape of the team, I had to ask him to go a little bit wide and he liked it.
"I was surprised he liked it because I would prefer to play him through the middle and the third goal showed you why he likes to play in that position.
"He was outstanding in his runs, power, ability, vision. So he's shown that he's improving all the time."
