The Blues saw Arsenal return to the top of the table with a 1-0 win at Newcastle but kept on their coat-tails with a pulsating display after falling behind to a third-minute Martin Skrtel goal.
Attacking midfield trio Oscar, Willian and Eden Hazard poured forward after the early setback and it was the Belgian who levelled things on 17 minutes with an exquisite right-footed equaliser which was curled beyond Simon Mignolet’s outstretched left hand.
Mignolet was at fault as Samuel Eto’o put the home side in front on 34 minutes after good work by Oscar, the Liverpool keeper failing to keep out the Chelsea striker’s tame close-range effort.
Liverpool pressed hard to get back level after half-time, Mamadou Sakho seeing a looping header come back off the upright and Luis Suarez having two penalty shouts turned down after clumsy challenges by John Terry and Eto’o.
The Blues always looked threatening on the break and had a chance to settle things through substitute Fernando Torres late on – but the former Reds favourite failed to beat Mignolet after a weaving run.
But Liverpool boss Brendan Rodgers – who lost Sakho, Glen Johnson and Joe Allen to injury during the game – may be left aggrieved by referee Howard Webb’s refusal to give his side at least one second-half spot-kick and to send off Oscar for a poor challenge on Lucas Leiva in stoppage time.
The result moves the Blues two points behind Arsenal in third place. Liverpool are six points off the pace at the halfway stage of the season.
The Reds led when Suarez got in front of Branislav Ivanovic to meet Philippe Coutinho’s free-kick. The ball hit Ivanovic and broke for Skrtel to tap in.
Conceding early roused Chelsea into action and Hazard forced Mignolet to save. Mignolet was at full stretch to turn over a Frank Lampard shot from 25 yards which appeared destined for the top corner – but the Belgian goalkeeper was beaten by a brilliant shot from his compatriot Hazard moments later.
Oscar drove through the middle and his attempted pass bounced off Sakho into Hazard’s path – and he hit a curled effort into the top corner.
Chelsea were now on top, but still had to be alert at the back and Gary Cahill made a brilliant tackle to deny Allen.
Ivanovic’s reunion with Suarez lasted less than half an hour after the Serbia right-back’s left leg over-stretched after he collided with Daniel Agger, with Ashley Cole replacing him and Cesar Azpilicueta moving to right-back.
Azpilicueta was involved in the move which took the Blues ahead, making an over-lapping run before Oscar crossed towards Eto’o – who got in front of Skrtel to poke in beyond Mignolet.
Lampard was replaced by John Obi Mikel as Jose Mourinho made his second change in a breathless encounter.
Sakho hit the bar with a looping header after being found by Jordan Henderson before Mignolet saved from Eto’o.
Suarez volleyed straight at Petr Cech after tangling with Mikel to earn his first shooting chance of the game and then went down in the box after competing for an aerial ball with Terry, with Webb unmoved.
Then Eto’o needlessly tripped Suarez – but again Webb dismissed Liverpool complaints.
Torres replaced Eto’o and immediately ran at the Reds, cutting in from the touchline before forcing Mignolet to save.
But the game ended with Brazil team-mates Lucas and Oscar involved in an angry exchange in stoppage time after the Chelsea man’s two-footed tackle.