United were clinical in front of goal but we deserved more after dominating long periods of the first hour.
We were in control of the first half but couldn't find the opening goal - Emmanuel Adebayor crucially had one disallowed - and then United hit us hard by scoring against the run of play just before half-time.
The second half followed the same pattern as we were on top again when the visitors grabbed a second goal on the hour.
Ashley Young's second goal for 3-0 ended the game as a contest although we had the consolation of Jermain Defoe's 25-yarder to make it 3-1 four minutes from time.
Harry Redknapp made three changes to the team that lost at the Emirates last Sunday.
Jake Livermore, Sandro and Aaron Lennon came in for Gareth Bale, who managed to overcome a hamstring problem but was ill overnight, suspended Scott Parker and Niko Kranjcar.
The teams shared efforts at goal in a lively start. Louis Saha shot straight at David De Gea, Danny Welbeck and Adebayor lashed over and Rooney's curler was easy for Brad Friedel - all inside 10 minutes.
De Gea was forced into serious action for the first time in the 19th minute when Adebayor picked up his poor clearance on halfway and drove into the box before aiming for the bottom corner. The Spanish goalkeeper read it and touched wide to his left.
It was all us in terms of possession with Sandro, Livermore, Luka Modric and Aaron Lennon excellent across the midfield.
Lennon was instrumental in carving open United in the 38th minute - leading to what we all hoped was the opening goal.
The winger skipped past Phil Jones and laid back for Saha to strike at goal. The ball was on its way in but hit Adebayor on the line and in the melee, the striker managed to backheel home.
But just as the celebrations started, referee Mr Atkinson whistled to disallow the goal for handball by Adebayor from Saha's initial shot.
Typically, after being second best for most of the half, United managed to get their noses in front on the stroke of half-time.
It was so straight forward as well as Young curled in a corner, Rooney found space six yards out and planted home his header.
First half stats showed up possession 58 per cent in our favour and we started the second half in the same fashion.
De Gea produced a fantastic save to palm out Livermore's 20-yarder and we were then closer still as Benoit Assou-Ekotto clipped the top of the crossbar with a free-kick from the edge of the box on 59 minutes.
But a minute later and we were hit with a hammer blow as Nani picked up Welbeck's throw on the right byline, his cross looped up and Young drilled a volley into the far corner.
Eight minutes later and it was all over as Young picked the ball up in space 25 yards from goal and curled a beauty into the top corner.
The game slowly petered after that but at least we gained some consolation as substitute Defoe picked up a wayward pass, ran 10 yards and fired past De Gea from 25 yards with four minutes left.
Spurs (4-4-2): Friedel; Walker, Kaboul, King, Assou-Ekotto; Lennon (Rose, 85), Livermore, Sandro (Kranjcar, 80), Modric; Adebayor, Saha (Defoe, 80). Unused subs: Cudicini, Dawson, Nelsen, Giovani.
United (4-3-3): De Gea; Jones, Evans, Ferdinand, Evra; Carrick, Scholes (Giggs, 60), Nani (Park, 80); Young, Rooney, Welbeck. Unused subs: Amos, Anderson, Hernandez, Fabio, Rafael.
Goals: Spurs - Defoe (86). United - Rooney (45), Young (60, 68).
Referee: Mr M Atkinson.