With 10 games left, United are now 12 points behind league leaders Arsenal and three behind second-placed Chelsea.
Unbeaten Arsenal were 2-0 winners at Blackburn Rovers on Saturday while Chelsea triumphed 2-0 at Bolton Wanderers.
After Sunday's defeat, United have only the FA Cup, where they face Arsenal in the semi-finals, as a realistic chance of silverware this season.
The result ended a traumatic week for United boss Alex Ferguson, who had a heart pacemaker fitted after their Champions League exit on Tuesday.
"It was a terrible result for us, you can't mask that and we obviously want to do something about it," he told Sky Sports TV.
"The important thing is to try to get our form back in terms of winning matches and eradicating these silly errors we are making at the back," added the Scot, whose side have taken just two points from their last four league games.
City took a surprise lead with a close-range goal by Robbie Fowler after three minutes and, after United looked to be taking control, doubled the lead when Jon Macken hooked the ball in from just inside the box after 32 minutes.
United pulled one back three minutes later when superb work by Ryan Giggs set up Paul Scholes to drive home his fourth goal in three games against City this season.
Giggs and Cristiano Ronaldo, a constant threat on the left, could have added more but, after City tightened up in the second half, they got their third in the 73rd minute, a blunder by Mikael Silvestre allowing Trevor Sinclair a chance he gleefully took.
SPECTACULAR SHOT
The hosts finished in style when Shaun Wright-Phillips lashed a spectacular shot into the roof of the net from wide on the right in stoppage time.
City manager Kevin Keegan was delighted with his team's third home league win this season and their second successive home derby success following their 3-1 victory in the last-ever clash at Maine Road last season.
"Today we showed the side of our character you need to beat teams like Manchester United -- the ability to stay with the game when it wasn't going our way," he said.
"Although you could say they will have better days, they won't have a better attitude and I think that's what got us back in the game.
"At 2-1, Manchester United started to play some wonderful football...people who right them off are foolish but we've edged them today.
"Everyone played a part, and none more so than the crowd. We've found it difficult to win here but I think they would swap all those disappointing days for what they've just seen out there."
Earlier on Sunday, Aston Villa cruised to an easy 4-0 win at midlands rivals Wolverhampton Wanderers.
They took the lead after six minutes through German midfielder Thomas Hitzlsperger and doubled in the 18th with an Olof Mellberg header.
Another blunder by the home side six minutes later gifted Villa a third goal to Juan Pablo Angel and the Colombian got his second on the hour after Villa keeper Thomas Sorensen had saved an Ioan Ganea penalty.
Newcastle United's hopes of climbing back into the top four were foiled at White Hart Lane when an 86th-minute own goal by Andy O'Brien gave Spurs a 1-0 win.
Liverpool were playing at Southampton in the day's other game.
