Goals from Didier Drogba and Thomas Vermaelen - at the wrong end - just before half-time did the damage for Carlo Ancelotti's side, who turned in a resolute defensive display before Drogba added a late third.
Earlier on Sunday, a Joseph Yobo own-goal and Dirk Kuyt's late strike gave Liverpool the spoils in a gritty Merseyside derby at Everton's Goodison Park. The first of three local derbies came at Molineux, where Lee Bowyer's early effort gave Birmingham a 1-0 win over Wolves.
On Saturday, Manchester City dropped points for the seventh straight Premier League match as they drew 1-1 with Hull. Shaun Wright-Phillips opened the scoring before a late Jimmy Bullard penalty earned a point for the visitors.
West Ham and Burnley served up a treat at Upton Park, with the home side emerging victorious in a 5-3 scoreline. The Hammers raced into a 5-0 lead, before the Lancashire outfit bagged three consolation goals, with ex-Red Chris Eagles on the