A late free-kick from substitute Vicente Rodriguez was enough to give the Seagulls maximum points and take them up to fourth, two points off the play-offs.
Poyet said: "This was a proper game in this division and, with none of the top 12 winning, we hope it's a turning point in terms of victories.
"I want us to be there at the beginning of April and it's totally up to us. It was important and the players fought for it.
"It's there for us to take and we're going to try. Make no mistake, this was a big win."
- Sports & Recreation