Chris Smalling opened the scoring after eight minutes, and Nani doubled the lead in the 37th.
The Red Devils have now won all five of their games in the league by a combined score of 21-4, and they lead second-place Manchester City by two points while holding a five-point edge on Chelsea.
Ashley Young's left-wing free kick created the first goal as his cross found the head of Smalling eight yards from goal and he redirected it past goalkeeper Petr Cech.
Chelsea squandered a great chance in the 26th minute when Torres set up Ramires for a shot from 10 yards with goalkeeper David De Gea out of position.
However, the Brazilian shot the ball straight back into De Gea with the net wide open.
The miss proved costly as Nani doubled the lead with a rocket from 20 yards that found the upper-left corner of the net, while Rooney benefited from a bit of luck just before the break to score the third goal.
John Terry attempted a clearance for Chelsea but it struck Nani and caromed into the path of Rooney, who was left with a simple finish from eight yards.
Nicolas Anelka came on as a substitute at halftime and he immediately set up a goal for Torres 30 seconds after the break.
Chelsea was the more dangerous side in the second half, but it was United that had the best chance to add to its lead as Nani was fouled inside the penalty area, but Rooney slipped while taking his spot kick and missed badly.
Fulham 2, Manchester City 2
London, England - Manchester City saw its perfect start come to an end on Sunday as the club was held to a 2-2 draw by Fulham at Craven Cottage after squandering a two-goal lead.
Sergio Aguero continued his fine start to the season by scoring in the 17th minute and then adding a second goal one minute after the break.
But City was unable to hold the lead as Bobby Zamora pulled the home side to within a goal and Danny Murphy equalized 15 minutes from time.
Tottenham 4, Liverpool 0
London, England - Tottenham won its second straight game on Sunday at White Hart Lane, defeating Liverpool 4-0 behind two goals from Emmanuel Adebayor.
Luka Modric put Spurs ahead after seven minutes, but Liverpool had Charlie Adam sent off in the 28th minute and Martin Skrtel also see red in the 63rd.
This opened the door for Tottenham to score three times in the final 25 minutes as Jermain Defoe scored his second goal of the campaign before Adebayor added two more.
Sunderland 4, Stoke City 0
Sunderland, England - Sunderland claimed its first victory of the season in resounding fashion on Sunday, handing Stoke City a 4-0 defeat at the Stadium of Light.
The opening 11 minutes of the match were a disaster for Stoke as Titus Bramble scored after four minutes and Jonathan Woodgate's own goal in the 11th made it 2-0 to the home side.
Craig Gardner added a third goal midway through the opening half and Sebastian Larsson capped the scoring for the Black Cats.