Chelsea added to Liverpool's away day woes with a hard-fought 1-0 win at Stamford Bridge.

Substitute Joe Cole's clever second half goal proved to be enough to give Chelsea all three points to help them close the gap on leaders Arsenal to two points and inflict a third successive Premiership defeat away from home on Liverpool.

Chelsea came racing out of the blocks and Jamie Carragher got in a vital block to deny Damien Duff getting a dangerous cross in, although in doing so he caught team-mate Chris Kirkland who looked to have picked up an injury, but the keeper was able to continue.

The home side continued to call the tune early on with Didier Drogba dragging a shot wide on five minutes before setting up Frank Lampard inside the box only for the midfielder to flash his shot wide of the target.

Chances were few and far between with the game becoming embroiled in a midfield battle and both defences on top.

Liverpool captain Sami Hyypia had a sight of goal on 22 minutes when he rose unmarked at the back post to Xabi Alonso's corner, but he could not direct his header on target.

Djibril Cisse had a half chance five minutes later when he beat John Terry to Harry Kewell's cross only to send his header well wide.

Drogba almost got through on goal on 28 minutes when he beat Josemi to Lampard's through ball, but he ran too wide allowing Kirkland to make a comfortable save.

Chelsea made an opening for Lampard on 34 minutes after a nice interchange between Alexei Smertin and Eidur Gudjohnsen, but the England midfielder failed to test Kirkland in the Liverpool goal.

Cisse, who was ploughing a lone role in attack, was unlucky with curling effort deflected just wide of the post by Chelsea full back Paulo Ferreira.

Chelsea suffered a major blow on 38 minutes when Didier Drogba was forced off with a stomach injury and had to be replaced by Cole.

Lampard missed a great chance to break the deadlock four minutes before the break when Ferreira got down the right and sent over an inviting cross for the midfielder who flashed his diving header well wide.

Cole was determined to make an impression in front of the on-looking Sven Goran Eriksson and five minutes after the restart he fired a shot into the side-netting.

Chelsea went close to opening the scoring on 57 minutes when Cole fired in a shot from the edge of the area which Kirkland palmed up into the air towards goal and was grateful to Harry Kewell, who cleared the ball off the line with his head.

The home side finally found a way through on 64 minutes with Lampard deceived the Liverpool defence with a low free kick into the box and Cole was on hand to expertedly volley the ball past Kirkland.

Carragher denied Chelsea a second goal on 69 minutes with a vital header under his own crossbar from the waiting Cole after Duff had got through and sent a dangerous delivery right across the six-yard box.

Djimi Traore made a crucial block six minutes from time to deny Gudjohnsen a second goal after Geremi had cleverly headed the ball down into the Icelandic's star path six-yards out.

Gudjohnsen wasted a fine opening three minutes from time to wrap up the match taking too long to take his shot and then eventually blazing his left-footed wildly over the crossbar.

Chelsea almost got Liverpool on the break in the last minute with Gudjohsen sending Cole clear on goal, but Hyypia got in a crucial block to keep out the midfielder's shot.

Liverpool substitute Steve Finnan forced Petr Cech into his first serious save of the match in stoppage time with a drilled shot from the right which the Czech keeper pushed out.