The Dane capped a rapid counterattack with a brave header to double the visitors' lead and although Danny Welbeck pulled one back a minute later, Tim Sherwood's men held on
Togo striker Adebayor opened the scoring in the 34th minute when he met an Eriksen cross, becoming only the third player to score in three consecutive games at the home of the Red Devils.
Eriksen doubled their lead in the 66th minute with a well-placed header after beating his marker, but Danny Welbeck brought United back into the game with his seventh goal of the campaign a minute later.
|VIEW FROM OLD TRAFFORD
|By Greg Stobart
Manchester United lose at home for the fourth time this season and there could have been no clearer signal for David Moyes to bring in signings to improve the squad in the January transfer window.
United were not terrible. They had chances late on and should have been awarded a penalty when Hugo Lloris clattered into Ashley Young.
But they are badly missing a dictator in central midfield and their record at Old Trafford this season simply isn’t good enough.
While Spurs rode their luck, they deserved to win here for the second successive season. They created the better clear chances, looked threatening on the counterattack and defended with spirit.
Emmanuel Adebayor scored a super header to put them ahead and the main concern for Tim Sherwood will be the severity of the injury that forced him off the pitch on a stretcher.
Christian Eriksen doubled the lead in the second-half with a poacher’s header and the Londoners showed great heart to keep their heads after Danny Welbeck put United back in the game and hugely boost their chances of Champions League football next season.
But chances for substitute Chicharito, Adnan Januzaj and Welbeck were all wasted as United slipped to seventh - 11 points behind leaders Arsenal - and saw their Premier League title hopes suffer a potentially fatal blow.
David Moyes made four changes in attacking positions to the United line-up from their victory over Norwich, with Wayne Rooney and Welbeck returning up front.
Kyle Walker and Danny Rose returned in the full-back positions for the visitors, with Etienne Capoue replacing the injured Paulinho in midfield.
Welbeck and Chris Smalling both had early chances for the hosts as United attacked down the right, but Hugo Lloris made good saves to keep Tottenham in the game.
The visitors had a fantastic chance to open the scoring in the 14th minute through Aaron Lennon, but the winger wasted a perfect throughball from Roberto Soldado as he fired straight at David De Gea.
With their next attack, in the 34th minute, Sherwood's side opened the scoring through Adebayor netting his third league goal of the season.
Eriksen raced down the right before delivering a perfect cross towards the back post, where Adebayor rose unmarked to score.
They should have doubled their lead five minutes later with another attack on the right.
This time, Lennon raced past Patrice Evra and played a low cross into the unmarked Soldado, but the Spaniard kneed the ball wide from six yards.
After a quiet start to the second half, the visitors doubled their lead in the 66th minute as Eriksen netted his second goal in three games.
The Dane anticipated the flight of a deflected Lennon cross far better than Antonio Valencia, stealing in front of the United man to head past De Gea from five yards.
However, United halved the deficit immediately through Welbeck.
Januzaj played a neat pass behind the Tottenham defence for the striker, and he latched onto the ball and calmly lifted it over Lloris.
The goal woke United up and Januzaj had a fantastic chance to level the game late on, but his long-range effort curled just wide of Lloris' right hand post.
That sparked a flurry of late chances to level, the best of which fell to Rooney and Nemanja Vidic, but they both found Lloris in excellent form as he saved well.