United beat Wigan Athletic 4-0 at Old Trafford with Paul Scholes among the scorers on his 700th appearance for the club, while Arsenal hammered Southampton 6-1 at the Emirates Stadium to hand the newly-promoted side a fourth successive defeat.
Chelsea stayed top of the table but lost their 100 percent record after their west London derby at Queens Park Rangers ended in a 0-0 draw.
Champions Manchester City also dropped points in a 1-1 draw at Stoke City where Peter Crouch put the home side ahead before Javi Garcia replied with his first goal for his new side.
Chelsea remain the early leaders with 10 points from four matches, followed by Manchester United (9), Arsenal (8) and Manchester City (8).
Swansea, who started the day in second place, slipped down to fifth after losing 2-0 at Aston Villa, while West Bromwich Albion, who were third at the start, lost 3-0 at Fulham where Dimitar Berbatov scored twice and Albion had Peter Odemwingie sent off in the first half.