Emmanuel Adebayor and Christian Eriksen did the damage in a 2-1 reverse despite Danny Welbeck giving David Moyes' side hope seconds after the visitors had doubled their lead in the 66th minute.
The Reds produced a high-tempo start with Welbeck twice almost released on goal and Hugo Lloris fortunate when a Chris Smalling drive squirmed under him but wide of his left-hand post. For all the hosts' impressive play, a warning was supplied by Aaron Lennon as he latched onto a Roberto Soldado pass to force David De Gea to save with his legs.
Spurs continued to threaten on the break and took the lead when Adebayor outjumped Smalling to plant a precise header into the corner of the net following Christian Eriksen's cross from the right. Soldado almost added a second but could not convert a Lennon centre.
After Danny Welbeck had a penalty appeal rejected, David Moyes threw on Shinji Kagawa and Javier Hernandez but the home side fell further behind when Wayne Rooney and Antonio Valencia, who had shifted positions to accommodate the changes, were unable to deny Lennon and Eriksen respectively with the Dane's stooping header beating De Gea.
It prompted an instant response from the restart as Welbeck raced onto an Adnan Januzaj pass to calmly dink the ball over Lloris to crank up the volume at Old Trafford. Januzaj saw a shot skip just wide and Spurs were forced to defend for their lives in the closing stages. Substitute Ashley Young was clearly caught by a high tackle by Lloris but again referee Howard Webb decided against pointing to the spot with Lloris also saving well from