Poyet's men welcome West Brom to the Stadium of Light with Sunderland two points ahead of third-bottom Norwich City in the battle to avoid the drop following a remarkable run of four games unbeaten that has included wins over Chelsea, Cardiff City and Manchester United.
Norwich face fourth-placed Arsenal in their final game of the season on Sunday, meaning that Sunderland, who possess a significantly superior goal difference, will likely only need a point from their game in hand against Pepe Mel's men to secure safety.
But Poyet insists he will not send his team out to play for a draw.
"I always thought it would go to the last minute of the last game, and we've got a chance now to finish it with a game in hand," said Poyet.
"The idea is to be concentrated on us, the way we've been in the last few games, don't change anything apart from going there and performing and playing and defending well and making it difficult for West Brom and winning the game.
"I don't know how to play a game to draw it or to get a point, the idea is to go and play. Then depending on the game, depending on the circumstances, you can make a decision to go a little bit forwards or a little bit backwards.
"We've put ourselves in an absolutely fantastic position, there is I don't know how many results in the games that we are going to play between us and Norwich.
"There is only one other side, and that is that we lose every game and Norwich beat Arsenal. If that happens, it doesn't matter what you've done before, you deserve to go down.
"We need to make sure that is not the point and the sooner we do it the better.
"We are very pleased but we need to get over the line."
