Martin Skrtel put the visitors up on just three minutes but Chelsea earned the points with goals from Eden Hazard and Samuel Eto’o.
An entertaining first half gave way to a steady second period but Chelsea’s defense held after the early leak.
It was a frantic opening to the match, with Liverpool capitalizing on an early opportunity. With Eto’o fouling Jordan Henderson early, Chelsea would concede on a set-piece yet again.
Philippe Coutinho sent in the long free kick, and Luis Suarez latched his head onto the back end before Skrtel cleaned it up with a tap-in for a shock lead on three minutes.
The goal didn’t phase the home side, as Chelsea worked for the equalizer forcing Glen Johnson to clear off the line after a Hazard shot from well out squirted through towards the goal mouth.
On 12 minutes Frank Lampard forced Simon Mignolet into action for the first time with a thunderbolt of a shot, causing the Liverpool keeper to dive to his left and get his fingertips on the ball to touch over.
They would get that equalizer in the 17th minute as they continued to ask questions of the Liverpool defense, and it would be the in-form Eden Hazard who would spring Stamford Bridge to life.
Oscar surged down the middle with the ball, and with Eto’o streaking to his right, Oscar looked to find him. Instead, the pass was blocked by Mamadou Sakho and fell right to Hazard who curled past Mignolet for a level score.
Jose Mourinho has struggled all year to find fluidity up front at the striker position, but Eto’o rewarded him for his selection in the 34th minute.
Again it was the Brazilian Oscar in the build-up, and as he scythed his way into the box, he cut the ball across the face and a sliding Eto’o finished by beating Sakho.
Chelsea were asked immediately to protect their lead, as Cech palmed away an effort from Joe Allen, giving the home side the advantage at halftime.
Having already brought off Branislav Ivanovic due to injury in the first half, Mourinho elected to substitute John Obi Mikel for Frank Lampard on the second half.
The first chance of the second period fell to Liverpool in the 51st, as a quick free kick went to Jordan Henderson, and his chip found Sakho in the penalty area, but the defender headed off the corner post. Chelsea then went right down and forced a fantastic save from Mignolet as Eto’o found space and rifled on goal.
Suarez got his first chance in the 58th minute on a beautiful cut-back cross from Henderson but the Uruguayan’s volley couldn’t avoid the waiting grasp of Petr Cech.
Liverpool found it hard to press through Chelsea’s defense, although Johnson popped off a bounding shot from distance in the 74th minute that Cech could only parry away.
Suarez protested mightily when Eto’o brought him down on the edge of the box, but it was off the ball and Howard Webb wasn’t biting.
The three points for Chelsea means the top three in the Premier League table all keep pace with wins, with Liverpool falling below Everton thanks to their second-straight 2-1 loss to a title contender.
Chelsea – Hazard 17′; Eto’o 34′
Liverpool – Skrtel 3′
Chelsea – Cech; Ivanovic (Cole 30′), Cahill, Terry, Azpilicueta; D Luiz, Lampard (Mikel 45′); Willian, Oscar, Hazard; Eto’o (Torres 87′).
Liverpool – Mignolet; Johnson (Aspas 84′), Agger, Skrtel, Sakho (Toure 90′); Lucas, Allen (Smith 60′), Henderson, Sterling, Coutinho; Suarez.