After a goalless first half, Spurs took control with their first goals at Old Trafford since winning there in January 2014.
Harry Kane put them ahead on 50 minutes with a powerful header from Kieran Trippier’s corner.
Two minutes and 13 seconds later, it was 2-0, Christian Eriksen crossing for Lucas to score.
Despite the entrance of Alexis Sanchez, United could not get a goal back and Lucas ran through their defence to make it 3-0.
Spurs go second on nine points behind Liverpool, while United are 13th.
Man Utd: 2 Sep v Burnley (A)
Spurs: 2 Sep v Watford (A)