Emmanuel Adebayor put Spurs ahead with a header in the 34th minute before lively playmaker Christian Eriksen turned from supplier to scorer on another quick counter-attack to leave United 2-0 down in the 66th.
Danny Welbeck responded a minute later with his fifth goal in his last five league matches but it was another tame home display by United, which is now 11 points behind leader Arsenal.
"The margin of error has been slim for a long time,'' United manager David Moyes said of his team's title hopes.
United has dropped more points after 20 games this campaign (26) than it did all last season (25), and notched just one win over the current top nine.
Visiting teams are coming to Old Trafford with more confidence and belief in the post-Alex Ferguson era. Tottenham was no exception and continued its revival under new manager Tim Sherwood, who has picked up 10 points from a possible 12 since replacing Andre Villas-Boas.
Spurs climbed above United into sixth, two points off fourth-place Liverpool.
"It is about letting (the players) have their head and go out and enjoy themselves,'' Sherwood said. "We have all played in the street. Sometimes you need to take it back to that.''
Adebayor has been central to Spurs' improvement, and he has now scored three goals and set up two others in his last four games since returning to the first team after being overlooked by Villas-Boas.
His goal was a classic striker's finish, drifting to the back post and beating back-pedaling fullback Chris Smalling with a downward header into the corner from Eriksen's pinpoint cross.
Aaron Lennon and Roberto Soldado squandered good chances in the first half and United's frustrations built, with Rooney booked for a blatant tug on Eriksen and Welbeck avoiding a yellow card despite a dive in the penalty area.
Moyes removed Smalling and holding midfielder Michael Carrick to go on all-out attack for the final 30 minutes but United was caught on the counter-attack for Eriksen's goal.
Adebayor launched the move and Soldado fed Lennon, who burst into the box and sent in a cross that deflected up off Nemanja Vidic. Eriksen nipped ahead of Antonio Valencia to head home from six yards out.
The two-goal cushion lasted barely a minute as Adnan Januzaj curled through a pass that Welbeck seized upon, before chipping the outrushing Hugo Lloris for a fine finish.
Spurs hung on in the final stages, with Lloris' reckless lunge at Ashley Young just inside the penalty area going unpunished. Moyes was incredulous at the decision of referee Howard Webb, saying: "I thought it was scandalous. It's a scandal.''
"You'd hope the people who put the referees out there would have a look at it and look to see if they think the referees are doing as well as they can be,'' Moyes added in a lengthy attack on Webb, arguably English football's top referee.
Spurs had gone 23 years without a league win at Old Trafford until a 3-2 victory last season. Now they have won there two seasons in a row.
Adebayor was carried off on a stretcher and Sherwood said he was unsure whether the striker would be fit to play against former club Arsenal in a north London derby in the third round of the FA Cup on Saturday.
"He has ice on everything,'' Sherwood said, without specifying the injury. "He doesn't know what is hurting him more.''