Jermain Defoe set the game alight within the first minute with a stunning overhead kick to put the home side in front but United refused to let it affect them.
Thrilling end-to-end football dominated the first half with both sides wasting opportunities to score. Spurs more than matched United in terms of attacking quality during the opening 20 minutes but Ryan Giggs scored the first goal of an inspiring comeback from a free-kick on 25 minutes.
From that point onwards, United grew into the game as Spurs failed to close down the opposition when they had the ball. The home side paid the price shortly before the half-time break as Anderson scored with a beautiful strike to notch his first goal in United's colours.
The start of the second half was littered with bookings and substitutions and when Paul Scholes was sent off for a second bookable offence, it seemed as if Spurs would take their chance of capitalising on their numerical advantage.
However, Sir Alex Ferguson introduced Michael Carrick, who brought composure to United's midfield. Peter Crouch had several great chances to score but, as time progressed, Spurs' tactic of sending crosses into their target man became sorely predictable.
Rooney eventually scored United's third in what was a perfect example of a counter-attacking goal and the away side will be content sitting in second place in the Premier League tonight.