Spurs had not beaten United since 2001 but wasted little time in showing their intent on this occasion when defender Jan Vertonghen struck a Gareth Bale pass into the bottom left corner of the goal in the second minute.
Bale doubled the advantage in the 32nd with his first goal of the season. The Welsh midfielder took a pass from Mousa Dembele near the center circle and made a diagonal run through the United half to his right before shooting across goalkeeper Anders Lindegaard into the bottom left corner.
Nani pulled one back from a Wayne Rooney cross early in the second half to start a flurry of three goals in three minutes.
Clint Dempsey restored Spurs' two-goal lead a minute later in the 52nd when he tucked in the rebound from a Lindegaard save of a Bale strike, but Shinji Kagawa immediately cut the visitors' lead to 3-2.
Tottenham endured a torrid half hour to end the match as goalkeeper Brad Friedel made a string of saves to preserve the win.
The result ended one of English football's longest winless streaks, as well as raising more questions over United's ability to regain the Premier League title as they slipped four points behind leader Chelsea, which earlier beat Arsenal 2-1 at Emirates Stadium.
Despite taking an early lead and twice leading by two goals, Tottenham never looked comfortable in the game.
Vertonghen opened the scoring when he strode between Nani and Carrick, drove into the United box and found the corner of Lindegaard's net.
The Belgian defender's shot took a significant deflection off Jonny Evans, but Vertonghen deserved his slice of good fortune for the adventure he had shown to take himself into a scoring position.
Rather than sting United into action, the early goal merely further encouraged the visitors.
Bale reveled in the open spaces between Paul Scholes and Rio Ferdinand, with the former looking all of his 37 years during a below-par first-half display.
When Robin van Persie lost possession on the edge of the Tottenham area, Dembele thundered upfield with purpose, leaving Scholes in his wake.
Bale took up the running from his teammate and duly sped past Ferdinand and into the box before beating Lindegaard to make it 2-0.
After resisting the temptation to name Rooney alongside Van Persie for the first time, United manager Alex Ferguson brought on the England forward to replace Ryan Giggs at the break.
The move helped trigger a burst of three quickfire goals.
Rooney provided the assist for Nani's close-range effort, curling a low cross to the near post that invited the clinical finish.
Van Persie could claim the credit for United's second as he threaded a precise pass through the Tottenham defence that allowed Kagawa to beat Friedel.
Crucially, though, Tottenham struck their third goal in between United's brace, Bale once again exposing poor defending as he surged forward, and when Lindegaard was unable to hold the Welshman's low shot, Dempsey was on hand to slot home the rebound.
Rooney thudded a brilliant free kick against a post before Van Persie's dismal attempt to finish off a Carrick pass suggested that it might not be United's day.
Tottenham needed to stand firm against the incessant wave of attacks.
William Gallas clattered into a post in an attempt to keep Nani's far-post cross away from Rooney, then Friedel turned away a Scholes strike.
Carrick's header almost sneaked in but dropped against the angle of post and bar instead.
United continued to surge, but it was not its day, after 23 years.
Courtesy of ScoreMobile (http://m.thescore.com/scoremobile)
Sent by Maxis from my BlackBerry® smartphone
