A late Fernando Torres double saw off a poor Chelsea side and kept Liverpool on the heels of league leaders Manchester United.
The Spanish striker struck twice in quick succession after Frank Lampard was harshly sent off for Chelsea.
But the sending off didnâ€™t mask Chelseaâ€™s ineffective performance - they had only a solitary shot on target throughout the whole match.
They had most of the gameâ€™s early possession but it was the hosts who had the most significant efforts on target in a first period that failed to sparkle.
Xabi Alonso forced Cech into a brilliant save with his powerful effort after 12 minutes. Six minutes later he was again called into action, this time by Javier Mascherano. The Argentineâ€™s effort was parried away by the Czech stopper.
Mascherano found himself in the refereeâ€™s notebook just a minute later after a series of niggly fouls.
Ashley Cole then became Chelseaâ€™s first recipient of a yellow card after bringing down Dirk Kuyt.
Cech was again called into action just after 25 minutes, smothering a Steven Gerrard shot with Kuyt close by.
John Terry then did well to block a Torres shot on goal.
At the other end of the pitch Chelsea were creating very little, with Salomon Kalou, Florent Malouda and Nicolas Anelka unable to keep a hold of the ball, let alone fashion any clear cut openings.
Brazilian defender Alex had Chelseaâ€™s most significant effort of the first half, sending a header over Pepe Reinaâ€™s goal from a Frank Lampard corner.
Albert Reiraâ€™s 42nd minute shot almost broke the deadlock when it hit Ashley Cole from Cechâ€™s parry, but thankfully for the England man the ball rolled wide of the post.
The red attacking tide continued into the second half. Kuyt sent the ball wide of the post and Alex - who was one Chelseaâ€™s only stand out performers - blocked a Torres shot.
Then on the hour mark Lampard received a straight red card for a studs up, sliding tackle on Xabi Alonso. The tackle seemed fair enough with the England midfielder appearing to win the ball. But to the astonishment of the Chelsea players, referee Mike Riley reached into his pocket and produce a red card.
The bemused expression on Frank Lampardâ€™s face said it all.
Alonso almost gave Liverpool the lead moments later, his shot struck Alex and looped over Cech but the ball hit the cross bar and Chelseaâ€™s keeper was able to knock the ball over to safety.
Chelsea needed some fresh legs to inject some life into a limp performance and Luiz Felipe Scolari sent on Didier Drogba and Deco in an attempt to provide it. The limpness continued. Deco and Drogba continuously lost possession and Liverpool began to lay siege to their opponents goal.
Mikel deflected another Torres effort over before Kalou had Chelseaâ€™s only effort on target - an angled shot that was comfortable for Reina.
Substitute Yossi Benayoun then had two shots as Liverpool continued to find Chelseaâ€™s strong rearguard action tough to break down.
Two minutes from time they finally found a way through. Fabio Aurelio played in a cross from the left wing and Torres beat Alex to the ball, and Cech at his near post.
The mercurial Spaniard doubled his tally in stoppage time, profiting from some slack defending from Ashley Cole. The left back carelessly gave possession away to Benayoun and the ball found its way to Torres, who completed the simplest of finishes.
There was a sour moment in the closing stages of the game when Jose Bosingwa needlessly dug his studs into Benayounâ€™s back near the corner flag. The defender could well face retrospective action from the FA.
Liverpoolâ€™s hopes of a first league title since 1990 remain very much alive, while Chelsea are left to count the cost of another disappointing performance against one of the â€˜Big Fourâ€™.