Goals from French duo Nicolas Anelka and substitute Florent Malouda after the break settled an absorbing contest high on commitment but lacking in clearcut chances.
Chelsea moved to 21 points, two ahead of champions Manchester United who were held to a draw by Sunderland on Saturday. A late own goal by Anton Ferdinand secured a 2-2 draw for United at home to Sunderland.
Sunderland were heading for their first win at Old Trafford since 1968 when defender Ferdinand deflected a left-foot drive from Patrice Evra into the net three minutes into added time. Earlier, Darren Bent gave the visitors a seventh-minute lead. Dimitar Berbatov pulled level in the 51st minute before Kenwyne Jones headed Sunderland back in front eight minutes later.
Sunderland defender Kieran Richardson was sent off in the 85th minute for kicking the ball away. Elsewhere, Hassan Yebda's header handed Portsmouth their first points of the season in a 1-0 win at promoted Wolverhampton Wanderers.
Tottenham Hotspur rose to third place with 16 points after 2-2 draw at Bolton Wanderers.
Ninth-placed Burnley beatBirmingham City 2-1 while Hull City beat (2-1) Wigan Athletic. On Sunday, Arsenal trounced Blackburn Rovers 6-2 after twice trailing in the first half of a sizzling encounter. The home side were stunned after four minutes when Steven Nzonzi headed Rovers in front before centre back Thomas Vermaelen drew Arsenal level with a thumping finish.
David Dunn's deflected shot after a counter-attack put Rovers back in front but this time their lead lasted just two minutes as Robin van Persie shot past Paul Robinson.
Russian Andrei Arshavin put Arsenal 3-2 ahead before halftime and the Gunners were rampant after the break, tearing Rovers to shreds. Cesc Fabregas capped a superb individual performance with a volleyed fourth, Theo Walcott slid in a fifth after an end-to-end move and substitute Nicklas Bendtner completed the rout when he rifled a shot in off the post.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks