Second half goals from Danny Welbeck, Anderson and Wayne Rooney sealed a comfortable victory for Alex Ferguson's youthful side, who went joint top of the table.
It marked defeat for Tottenham in their opening game of the season after their first fixture of the new campaign was canceled due to the London riots.
Victory took United level at the summit with rivals Manchester City, who maintained their 100 per cent record with a 3-2 win at Bolton on Sunday.
Tom Cleverley was the first to test Tottenham's goalkeeper Brad Friedel as the veteran American turned his goal-bound effort round the post before Ashley Young went close with a looping header from Rooney's cross.
Jermain Defoe and Gareth Bale both tested United's Spanish keeper David De Gea in the second half before Welbeck broke the deadlock on the hour with a firm header from Cleverley's right wing cross.
Welbeck was also heavily involved in the second goal as his back-heel wrong footed Tottenham's defence and Anderson slotted the ball into an empty net.
Rooney then grabbed his second of the season as he nodded home Ryan Giggs' cross from seven yards out.
Man Utd De Gea,Smalling,Jones,Evans,Evra,Nani,Cleverley (Giggs 81),Anderson,Young (Park 81),Rooney,Welbeck (Hernandez 81).
Subs Not Used: Lindegaard,Berbatov,Carrick,Fabio Da Silva.
Tottenham Friedel,Walker (Corluka 46),Dawson,Kaboul,Assou-Ekotto,Lennon,Livermore (Huddlestone 74),Kranjcar (Pavlyuchenko 74),Bale,Van der Vaart,Defoe.
Subs Not Used: Gomes,Jenas,Bassong,Townsend.
Att: 75,498
Ref: Lee Probert (Wiltshire).