Chelsea came from behind to beat Liverpool 2-1 at Anfield in the Premier League on Saturday, while Manchester United won 1-0 against Crystal Palace thanks to a goal from Juan Mata.
Emre Can put Liverpool ahead in the seventh minute with a long-range strike that deflected off Gary Cahill, before Cahill reacted quickest to a rebound from John Terry's header five minutes later to equalize, although the goal needed confirming through goal-line technology.
Diego Costa scored in the second half to secure Chelsea's win.
Elsewhere, Mata scored from 20 yards in a needed victory for United, and Shane Long scored both in Southampton's 2-0 win against Leicester.
Burnley won for first time this season, 1-0 against Hull, while West ham drew 0-0 with Aston Villa.