Goals from Emmanuel Adebayor and Christian Eriksen put Tottenham in control and, although Danny Welbeck pulled a goal back, Tim Sherwood's men held on for an impressive win.
The defeat was United's sixth in the Premier League this season and leaves them 11 points behind leaders Arsenal.
For Tottenham it was their third victory in four games under Sherwood as they moved above United in the table to sixth to boost their top four hopes.
United started on the front foot and went close to scoring after just five minutes when Welbeck got in behind the Spurs defence, but Hugo Lloris did well to snuff out the danger.
Moments later Chris Smalling burst into the box and fired in a shot which squirmed under the legs of Lloris and behind for a corner.
Tottenham almost broke the deadlock on 13 minutes with their first attack of the game as Roberto Soldado threaded a fantastic ball through to Aaron Lennon inside the box, but the winger saw his shot blocked by the legs of David de Gea.
United continued to push forward in search of the opener, winning a succession of corners, and from one Nemanja Vidic saw his header fall wide of the target.
Adebayor had a sight of goal on 32 minutes when the ball sat up nicely to him on the edge of the box and he flashed his half-volley over the crossbar.
Two minutes later Spurs stunned the home side with Adebayor netting his fourth goal of the season as he rose above Smalling to head home Eriksen's inviting cross into the bottom corner past De Gea.
Spurs wasted a great chance to double their lead six minutes before the break when Adebayor sent Lennon in down the right and he fired over a cross which Soldado knocked wide with his shin with the goal at his mercy.
Welbeck had a sight of goal five minutes after the break when Michael Carrick picked him out inside the box, but the striker failed to get enough power on his effort to trouble Lloris.
Spurs doubled their lead on 66 minutes when Eriksen capitalised on some poor defending from Antonio Valencia to get on the end of Lennon's deflected cross to head home past De Gea from six yards.
United pulled a goal back almost straight away as Adnan Januzaj split the Spurs defence to find Welbeck inside the box and the striker clipped his shot over Lloris to give the home side hope.
United laid siege to the Spurs goal in search of an equaliser and Januzaj curled a shot just wide before substitute Javier Hernandez saw his flick saved by Lloris.
The home side threw everything at Spurs in the closing stages with Rooney seeing his shot saved by Lloris and the goalkeeper survived a penalty appeal after his challenge on substitute Ashley Young.
Vidic then saw his header kept out by the Spurs keeper as the visitors held on for all three points to increase the woes of United boss David Moyes.