Chelsea cut the gap behind leaders Arsenal back to four points after they came from behind to beat Southampton 3-1 at Stamford Bridge.
Jose Mourinho's side had been stunned when Jay Rodriguez opened the scoring after just 13 seconds.
Michael Essien, making his first league start of the season, was at fault and was hooked at half-time with his side still behind.
Demba Ba was brought on and he completed a second-half turnaround after central defensive duo Gary Cahill and John Terry had both scored with headers.
Champions Manchester United are nine points off the pace after they twice came from behind to draw 2-2 at Tottenham.
Under-fire Spurs boss Andre Villas-Boas saw his side go ahead through Kyle Walker and a stunning Sandro strike but Wayne Rooney pegged them back on both occasions.
Samir Nasri also struck twice as Manchester City beat Swansea 3-0 to move up to third.
Alvaro Negredo opened the scoring on eight minutes before Nasri made the points safe in the second half.
Liverpool slipped from second to fourth following a shock 3-1 defeat at Hull.
Reds skipper Steven Gerrard had cancelled out Jake Livermore's heavily-deflected opener, but Hull scored twice in the final 18 minutes.
David Meyler fired them ahead again before Martin Skrtel directed in a weak Tom Huddlestone effort that looked to be off target.
Hull had never beaten Liverpool before in their history and the three points moved them into the top half.