Jan Vertonghen and Gareth Bale gave the visitors a deserved half-time lead.
Not for the first time at Old Trafford in recent years, Spurs were hit by a fierce second-half fightback.
However, amid a flurry of goals, Clint Dempsey scored in between efforts from Nani and Shinji Kagawa. And, after Wayne Rooney and Michael Carrick had struck the frame of Brad Friedel's goal, Andre Villas-Boas' side clung on for the final whistle to register a thrilling 3-2 Barclays Premier League triumph at Old Trafford.
The result lifted Spurs to fifth in the table - one point behind third-placed United and five adrift of leaders Chelsea, who finished the day three points clear after winning 2-1 at Arsenal in the lunchtime kick-off.
Blues captain John Terry came through a hostile reception at the Emirates Stadium as Roberto Di Matteo's side consolidated their lead.
Fernando Torres fired the visitors ahead following some poor marking by Laurent Koscielny and Juan Mata's free-kick squirmed in to secure three points for the European champions after Gervinho had equalised on the stroke of half-time.
Manchester City striker Edin Dzeko struck a late winner as the champions came from behind to win 2-1 at Fulham.
Dzeko slotted home the decisive goal three minutes from time after Sergio Aguero had cancelled out Mladen Petric's early penalty.
Aguero tapped home the follow-up after Mark Schwarzer had parried Carlos Tevez's deflected shot two minutes before the interval.
Petric had sent England goalkeeper Joe Hart the wrong way from the spot after Pablo Zabaleta's foul on John Arne Riise.
In Saturday's other 3pm kick-offs, Luis Suarez netted a Carrow Road hat-trick for the second straight season as Liverpool romped to a 5-2 success against Norwich.
The Uruguay striker opened the scoring with a clinical right-footed finish in the second minute and then, seven minutes before the interval, dispossessed Michael Turner and despatched a superb curling shot with the outside of his right foot past John Ruddy to give the Reds a two-goal half-time lead.
Suarez turned provider within two minutes of the restart as on-loan Real Madrid midfielder Nuri Sahin's first Premier League goal extended the visitors' lead, and then completed his treble with another fine curling effort.
Steve Morison pulled one back just after the hour mark but Steven Gerrard's deflected strike midway through the second half restored the Reds' four-goal cushion.
Grant Holt then slid his first goal of the campaign past Jose Reina three minutes from the end but it was scant consolation for the well-beaten Canaries.
Nikica Jelavic notched twice as Everton wrapped up a 3-1 win over Southampton before half-time after the Saints had taken an early lead through Gaston Ramirez's first goal for the club at Goodison Park.
Leon Osman latched onto a loose ball in the penalty area to smash home the equaliser before Jelavic's brace gave the Toffees a half-time cushion.
The Croatia forward first fired a left-footed shot across Paulo Gazzaniga and then directed a powerful header past the Southampton goalkeeper seven minutes before half-time.
Reading's clash with Newcastle burst into life after the break after a goalless first 45 minutes, Demba Ba maintaining his impressive start to the campaign with two more goals in a 2-2 draw.
The Royals opened the scoring in fortuitous fashion when Jimmy Kebe miscued a shot into the bottom corner in the 58th minute, but Ba's sublime volley restored parity for the Magpies a minute later.
Noel Hunt's header in the 62nd minute from Jobi McAnuff's cross put the hosts ahead for the second time, but again Ba equalised - the Senegal forward's header allowed to stand despite a hint of handball.
Sunderland striker Steven Fletcher continued his fine scoring run since his summer move from Wolves with the winner as the Black Cats toppled 10-man Wigan 1-0 at the Stadium of Light.
After an uneventful first half the game brightened up after the restart when Latics midfielder Jordi Gomez was sent off for a nasty challenge on on-loan Tottenham full-back Danny Rose.
The Black Cats took only four minutes to make their extra man count, Fletcher turning home James McClean's cross-shot for what turned out to be the winner.
Stoke's Peter Crouch was at the double to give his team a 2-0 triumph against Swansea at the Britannia Stadium.
The 6ft 7in frontman headed home the opener after 12 minutes and then tapped in a second nine minutes before the break.
Saturday's Premier League Results
Arsenal 1-2 Chelsea
Norwich 2-5 Liverpool
Man Utd 2-3 Tottenham
Fulham 1-2 Man City
Sunderland 1-0 Wigan
Everton 3-1 Southampton
Reading 2-2 Newcastle
Stoke 2-0 Swansea
Sunday's Premier League Fixtures
Aston Villa vs West Brom
Monday's Premier League Fixtures
QPR vs West Ham