The Black Cats' success contributed to Fulham and Cardiff's relegation and lifted them three points above Norwich with a superior goal difference and two games left to play.
Seb Larsson scored the only goal of the game in the 30th minute and the margin of victory could have been greater with both Emanuele Giaccherini and Fabio Borini hitting the woodwork in the second half.
Poyet told Sky Sports: "It is difficult to explain - incredible, unique, special.
"The determination of the players, they were willing to do things right - what a game of football we played here.
"It was very difficult today, it was tough. There were moments that we looked very tired, but somehow we coped with that as a team. The clean sheet today is immense.
"It was difficult in the beginning, the game looked a little bit flat. I was a bit worried because it is important for us to compete.
"The goal gave us that extra bit that we need and then in the second half we knew if Manchester United made a few changes and were coming forward there would be space.
"We needed to pass the ball and we needed to believe - at the right time, not all the time, we also needed to defend.
"I said a few days ago, if we get another three points and stay up it is going to be an absolutely incredible season.
"At the right times we have come back and we have done something special."
Norwich travel to Chelsea on Sunday, live on Sky Sports 1HD, and former Chelsea player Poyet is keen for his old club to do his current employers a favour.
Victory for the Blues would effectively seal the final relegation spot for the Canaries, as their goal difference is currently 13 worse than Sunderland's, who host West Brom in midweek.
He added: "I hope my team give me a hand tomorrow. We are going to watch the game tomorrow at four o'clock.
"If they (Norwich) don't win and we are safe before that, it's life. We must concentrate, rest and we will be back for Wednesday."