Sebastian Larsson converted Connor Wickham's cross on the half-hour to seal a 1-0 victory at Old Trafford which puts the Black Cats within touching distance of safety.
If Norwich lose at Chelsea on Sunday, Sunderland need only one point from home matches against West Brom or Swansea to send the Canaries down and ensure their own top-flight survival.
Even if Sunderland lose their final two games, there needs to be a huge swing of goals in Norwich's favour to keep the Norfolk club up should they fail to pick anything up at Stamford Bridge.
Less than three weeks ago, Sunderland were seven points from safety with games to come against Chelsea, United and Manchester City.
So there is little wonder that Gus Poyet believes a little divine intervention has helped his team take 10 points from a possible 12.
"This is close to a miracle," the Sunderland manager said.
"A miracle was the word I used a few weeks ago and apparently every now and again it happens.
"We thought we would have to win four matches after losing to Everton (on April 12).
"We won three and if we win one (more) we are over the line
Chelsea could help us tomorrow
I don't know if I will be able to watch.
"What we have done in the last four games is unique.
"It is special, incredible...
"We were getting no breaks
Normally that sends you down, and then you need something very special."
After victories over Chelsea and Cardiff, as well as a point that could have so easily been a win at Manchester City, Sunderland now have the scalp of United in the bag.
This win was no fluke
After beating Norwich on a nostalgic afternoon last weekend, the stage was set for Ryan Giggs to coast to his second successive win as interim boss.
But Sunderland are made of far sterner stuff than the Canaries.
The Black Cats dominated United's midfield, they kept the hosts' club-record signing Juan Mata quiet, and they showed their clinical side when Larsson swept home Wickham's cross following some shoddy marking by Michael Carrick and Darren Fletcher.
Had Emanuele Giaccherini and Fabio Borini found the net instead of the woodwork, the boos that rang out from the home fans at the final whistle would have been even louder.
Poyet has led Sunderland to almost certain safety and a League Cup final since he took over from Paolo Di Canio in October 2013, but he insists the players should take the credit for dragging the team out of the relegation zone.
"We have done it because of the players," the former Brighton manager said.
"They came together, they believed, and they defended for their lives.
"We have 10 players out of contract (in the summer).
"It would have been easy for them to give up and think about next year, the next challenge, the next club.
"But they are here, they are fighting for the club and the fans
They don't want to go down
They are not going to accept it
That makes me feel very proud."
Giggs would be forgiven for having no pride in his players after this defeat.
United lacked tempo, their passing was poor and they could not find a way through a defence that has shipped 57 goals this season.
The feel-good bubble that surrounded Old Trafford following the interim appointment of Giggs and his fellow Class of '92 graduates has now burst.
"I feel flat, the players were a bit flat, and I don't know why," the Welshman said.
"We controlled possession but we just lacked that quality in the final third, and concentration."
United have now lost seven times at Old Trafford this year
Stoke, West Brom and Norwich have better home records.
For a man who is used to winning game after game at Old Trafford, Giggs admits such a poor record is hard to take.
"We have shown good form away from home but at Old Trafford seems to have been a problem," the 40-year-old said.
"In past seasons there would be waves and waves of shots and saves and you could always sense a goal was coming but this season it doesn't seem to have happened."
Giggs, who is out of contract in the summer, has yet to decide whether he will play in Tuesday's match against Hull.
With Louis van Gaal set to be appointed as David Moyes' successor, there is no guarantee that Giggs will be around next year.
Wayne Rooney may take to the field on Tuesday after he was left out against Sunderland due to a groin problem, though.
"We will keep monitoring him and see how he is for Tuesday," Giggs said.
"Hopefully he will be back."
Source : PA
Source: PA