Chelsea's Eden Hazard celebrates with teammates after scoring his team's opening goal against Liverpool during their Premier League match on December 29, 2013 © Getty Images

It was the visitors who struck first, breaking the deadlock just four minutes into the clash when Martin Skrtel tapped in from a Philippe Coutinho free kick.

Eden Hazard and Frank Lampard both had shots saved as they sought a quick equaliser for the hosts, but the Belgian managed to find the target with a curling effort from the edge of the box after 18 minutes.

Chelsea looked the stronger of the two sides for the remainder of the first half and managed to take the lead 10 minutes before the break when Samuel Eto'o tapped in from an Oscar cross.

Chelsea's Samuel Eto'o celebrates after scoring his team's second goal against Liverpool during their Premier League match on December 29, 2013 © Getty Images

Joe Allen came close to leveling for the Brendan Rodgers's side, but Petr Cech punched the ball away to keep his team ahead.

Liverpool made a bright start to the second half, with Mamadou Sakho rattling the bar just seven minutes after the restart.

Eto'o responded to Liverpool's attacking start by racing down the other end of the pitch and attempting to smash the ball past Simon Mignolet, but the Reds' keeper tipped the ball away on the stretch.

Chelsea had kept the Premier League's leading scorer, Luis Suarez, quiet for much of the opening hour, but the Uruguayan unleashed a shot in the 57th minute, trying to volley in from a Jordan Henderson delivery; however, once again Cech had it covered.

The visitors continued to press for a second goal to level the score, but a 25-yard effort from Glen Johnson was not enough to beat the Chelsea keeper.

Former Liverpool striker Fernando Torres came off the Chelsea bench late on and came close to putting the result beyond doubt, but his shot went straight into the hands of Mignolet.

The result leaves Chelsea two points off the top of the table, while Liverpool drop to fifth.