Sebastian Larsson took advantage of some slack marking to fire home Connor Wickham's cross in the first half as Sunderland recorded their first win at Old Trafford since 1968.
What had been billed as a tough fixture turned out to be something of a stroll for the 1-0 winners.
Fabio Borini and Emanuele Giaccherini both struck the woodwork in the second half and Gus Poyet's team looked comfortable in possession all afternoon.
The win condemned Cardiff and Fulham to relegation, while Sunderland are now big favourites to stay in the Barclays Premier League too.
Providing Norwich lose at Chelsea on Sunday, the Black Cats need only to take one point from their final two matches to survive.
And after recent wins over Chelsea, Cardiff and now United, few would back against the Wearsiders to do so.
This was the afternoon that the feel-good bubble surrounding Giggs well and truly burst.
The high-tempo, counter-attacking football he demanded from his players was absent all day.
United were flat in midfield, Javier Hernandez went missing up front and even the return of Robin van Persie from the bench could not inspire the Red Devils to victory.
Many United fans wanted Giggs to be the club's next manager, but the board are wise to turn to the more experienced Louis van Gaal, who is set to be appointed as David Moyes' successor next week.
United's defeat also highlighted the need for reinforcements this summer, particularly in midfield, where Nani, Darren Fletcher and Michael Carrick failed to impress.
The number of empty seats visible at the final whistle was remarkable. The small pocket of away supporters had every reason to remain and hail their team, who are almost safe just a few weeks after looking doomed.
It was all smiles for the home fans just before kick-off when Giggs received another huge welcome as he strolled down the touchline to his seat in the dugout.
But just as they did in like last week's win over Norwich, Giggs' men started very slowly.
Ashley Young, one of five changes to a starting XI that did not contain the injured Wayne Rooney, dazzled Marcos Alonso with his skill, but his final ball was poor.
The only time United came close to scoring in the opening 15 minutes was when John O'Shea nearly turned the ball into his own net from Carrick's cross.
Another United old boy - Wes Brown - then put a crucial block in to deny Nani, who then picked himself up before curling over from 20 yards.
Patrice Evra bundled his way through the crowd, but his weak header was easily collected by Vito Mannone.
It was all a bit lacklustre from the hosts.
Young and Nani used their trickery to try to get past their markers, but there was no one in the box to convert.
Hernandez, making his fifth league start of the year, dropped too deep, leaving United without a focal point up front.
Giggs had seen enough. With 26 minutes on the clock he came to the touchline for the first time to stand over his players.
Four minutes later his mood worsened as Sunderland took the lead.
Fletcher inexplicably allowed Wickham to send over a cross which Larsson expertly finished after giving Carrick the slip.
If Giggs hoped that would kick his team into gear then he was wrong.
United were just as flat and unimaginative until the break, with Juan Mata the only man to test Mannone courtesy of a low drive.
Soon after the restart the United fans started voicing their frustration as the home team passed the ball across midfield without, seemingly devoid of any idea how to pierce the Sunderland back four.
United upped the tempo briefly near the half way point of the second period. Evra crossed for Hernandez, but Brown intervened just as the Mexican was about to shoot.
Nemanja Vidic appealed for a penalty when his header struck Lee Cattermole in the box, but Howard Webb waved play on.
Giggs replaced Nani with Adnan Januzaj, who scored two goals in the reverse fixture.
Then Van Persie entered, along with Danny Welbeck, for his first game in more than six weeks.
Sunderland should have put the result beyond doubt with 17 minutes to go, but Giaccherini's weak shot from a cross by fellow substitute Jozy Altidore hit a post and bounced out to safety.
A huge amount of United fans headed for the exits 10 minutes before the end.
Borini almost made it 2-0 when he struck the bar, but one goal proved enough for Poyet, who jumped for joy when the final whistle went.
A large number of the United fans who remained booed their team off.
The manager may have changed, but the club's awful home form continues.