Chris Smalling gave United the lead in the eighth minute when he latched on to the end of Ashley Young's curling free-kick.
Nani added the second to mark his 100th league game for United, blasting home an unstoppable shot from 25 yards, before Wayne Rooney capitalised on Chelsea's failure to clear the ball to score from point-blank range just before half-time.
Fernando Torres got one back for Chelsea a minute into the second half after substitute Nicolas Anelka put him through on goal with an inch-perfect pass.
Rooney slipped and missed a penalty after Nani was brought down by Jose Bosingwa in the 57th minute, before Torres missed an even easier chance when he completely miscued his shot in front of an open goal.
Earlier, Fulham came from two goals down to deny Manchester City victory in the 2-2 draw at Craven Cottage.
Sergio Aguero fired City into a two goal lead before goals by Bobby Zamora and Danny Murphy earned the Cottagers a point.
Argentinian Aguero scored his first in the 18th minute after Gareth Barry and David Silva linked up in midfield to put the striker through on goal.
He added the second, his eighth goal of the season, just seconds into the second half.
Fulham clawed one back thanks to a curling shot by Zamora from the edge of the box after 55 minutes before Murphy levelled the score for the Cottagers when his 25-yard shot took a big deflection off Vincent Kompany and flew past Joe Hart.
At White Hart Lane, Tottenham surged to a 4-0 win over nine-man Liverpool thanks to goals by Luka Modric, Jermain Defoe and two for Emmanuel Adebayor.
Charlie Adam and Martin Skrtel both saw red for the visitors after picking up two yellows cards.
Modric scored the opener in the seventh minute with a fine shot into the top corner. Adam was then sent off just before the half hour when he picked up a second yellow for catching Scott Parker on his thigh.
Liverpool's woes increased in the 63rd minute when defender Skrtel was sent off after a careless tackle on Bale.
Defoe added Tottenham's second after Rafael van der Vaart put him into acres of space, allowing him to turn past Jose Enrique before blasting the ball into the net.
Adebayor slotted home the third before adding the fourth in stoppage time.
Sunderland beat Stoke 4-0 at the Stadium of Light to record their first win of the season.
Titus Bramble opened the scoring in the fifth minute before Jonathan Woodgate doubled the Black Cats' lead with a headed own-goal.
Craig Gardner made it 3-0 on the half-hour, beating a tackle from Ryan Shawcross to loop his shot over Asmir Begovic from the edge of the box.
Sebastian Larsson added the fourth from a free-kick on 58 minutes to complete the rout.
Manchester United 3-1 Chelsea
Tottenham 4-0 Liverpool
Fulham 2-2 Manchester City
Sunderland 4-0 Stoke
Blackburn R. 4-3 Arsenal
Aston Villa 1-1 Newcastle U.
Bolton W. 1-2 Norwich C.
Everton 3-1 Wigan Athletic
Swansea C. 3-0 West Bromwich A.
Wolverhampton W. 0-3 Queens Park R.