Antonio Conte's Chelsea side were rocked by Marcus Rashford's early goal and a deflected Ander Herrera strike soon after half-time at Old Trafford delivered a major blow to their title ambitions.
The Blues barely managed an attack of note and a second defeat in their last four league games leaves them clinging to a four-point lead over second placed Tottenham, who had piled on the pressure with a 4-0 rout of Bournemouth on Saturday.
After appearing set to cruise to the title for most of the season, Chelsea now face a nerve-jangling final six matches as they try to hold off a strong challenge from their London rivals.
It was a sweet moment for United manager Jose Mourinho, who had suffered a 4-0 thrashing against Chelsea in October on his first return to the club since being sacked last season.
United were also knocked out of the FA Cup quarter-finals by Chelsea last month and avenging those painful losses kept alive their bid to qualify for the Champions League via a top four finish.
Mourinho's men, unbeaten in their last 22 league games, are now fifth, four points behind fourth placed Manchester City with a game in hand.
Chelsea's cause wasn't helped by the absence of goalkeeper Thibaut Courtois, who was injured earlier in the week, and the pre-match withdrawal of left wing-back Marcos Alonso due to a reported illness.

Manchester United's Ander Herrera scores their second goal
Reuters And the Blues looked less solid than usual at the back as United carved them open to take the lead in the seventh minute.
It was a goal rooted in controversy from Chelsea's point of view as United midfielder Herrera appeared to handle to win back possession.
Even so, Chelsea defender David Luiz was still exposed too easily by Herrera's precise pass, with Rashford allowed to gallop clear before slotting a cool finish under Asmir Begovic for his ninth goal of the season.
United, whose leading scorer Zlatan Ibrahimovic started on the bench, were rewarded for a vibrant display when they struck again in the 49th minute.
Ashley Young's persistence opened space for Herrera and the Spaniard's shot from the edge of the penalty area deflected off Chelsea defender Kurt Zouma before looping over Begovic.
At the Hawthorns, Liverpool playmaker Roberto Firmino settled a scrappy game with a close-range header in first half stoppage-time to condemn Albion boss Tony Pulis to his first ever home league defeat against the Reds.

Liverpool's Roberto Firmino scores the winning goal against West Bromwich Albion
ReutersThe Brazilian converted a flick-on from Lucas Leiva to seal Liverpool's fifth win in their last seven games.
Liverpool are unbeaten since losing at Leicester in late February and now lead City by two points, although Pep Guardiola's team have a game in hand in the race for an automatic spot in the Champions League group stage.
With United, Arsenal and Everton also still in contention for a top four finish, Liverpool boss Jurgen Klopp isn't getting carried away just yet.
"It is the Premier League, Arsenal have three games in hand so we should not think about this," Klopp said.
"Today we could only get to 66 points, so it feels perfect. Next week we try at Anfield to get 69, and let's carry on.
"If we do what we have to do we will be where we want to be."
RESULTS:
Manchester United 2 Marcus Rashford 7, Ander Herrera 49
Chelsea 0West Bromwich Albion 0 Liverpool 1 Roberto Firmino 45+1
Saturday, April 15
Southampton 0 Manchester City 3 Vincent Kompany 55, Leroy Sane 77, Sergio Aguero 80
Sunderland 2 Wahbi Khazri 26, Fabio Borini 90
West Ham United 2 Andre Ayew 5, James Collins 47
Stoke City 3 Marko Arnautovic 6, Peter Crouch 66, Xherdan Shaqiri 80
Hull City 1 Harry Maguire 51
Everton 3 Phil Jagielka 49, Ben Mee 71og, Romelu Lukaku 74
Burnley 1 Sam Vokes 52pen
Watford 1 Etienne Capoue 42
Swansea City 0Crystal Palace 2 Yohan Cabaye 54, Christian Benteke 69
Leicester City 2 Robert Huth 6, Jamie Vardy 52
Tottenham Hotspur 4 Dembele 16, Son Heung-Min 19, Harry Kane 48, Janssen 90+2
Bournemouth 0Standings P W D L F A
Pts1
Chelsea 32 24 3 5 65 27
752
Tottenham Hotspur 32 21 8 3 68 22
713
Liverpool 33 19 9 5 69 40
664
Manchester City 32 19 7 6 63 35
645
Manchester United 31 16 12 3 48 24
606
Everton 33 16 9 8 60 37
577
Arsenal 30 16 6 8 61 39
548
West Bromwich Albion 33 12 8 13 39 42
449
Southampton 31 11 7 13 37 40
4010
Watford 32 11 7 14 37 52
4011
Stoke City 33 10 9 14 37 48
3912
Leicester City 32 10 7 15 41 53
3713
West Ham United 33 10 7 16 44 59
3714
Burnley 33 10 6 17 33 47
3615
Crystal Palace 32 10 5 17 44 52
3516
Bournemouth 33 9 8 16 45 63
3517
Hull City 33 8 6 19 34 67
3018
Swansea City 33 8 4 21 37 68
2819
Middlesbrough 31 4 12 15 22 37
2420
Sunderland 32 5 6 21 26 58
21