Fernando Torres scored his first goals since October to keep Liverpool's title dreams alive.
Rafael Benitez's side still trail Manchester United by two points having played a game more, but remain in the hunt after eventually overcoming stubborn Chelsea resistance.
Chelsea had Frank Lampard sent off in the second half and from then on Liverpool pounded away in search of the winner.
And Torres struck with a near-post header and a simple tap in the final minutes.
Liverpool made three changes from the side which drew at Wigan in midweek, with Albert Riera, Dirk Kuyt and Xabi Alonso returning in place of Yossi Benayoun, Ryan Babel and Lucas.
Striker Robbie Keane was omitted from the 18-man squad, with teenage striker David Ngog on the bench.
Chelsea fielded the same side which beat Middlesbrough 2-0 in midweek, with Salomon Kalou passed fit.
Keane did not attend Anfield the last time he was left out of a squad, but was all smiles going into the home dressing room this time, and sat in the directors' box later.
But suggestions that he is on his way out of the club cannot be discounted and there was plenty of interest in the other goings on in the stands before the game, with co-owners George Gillett and Tom Hicks sitting well apart in the front row of the directors' box.
The pair will be re-opening talks with Benitez over his new contract and attend a board meeting together tomorrow.
On the pitch the game started in swirling snow, with Steven Gerrard surging around midfield as Liverpool took the game to Chelsea.
Alonso forced the first save from Petr Cech after 11 minutes, seeing a 20-yarder tipped over. Then Javier Mascherano fired in a low 30-yarder that Cech parried away, with no Liverpool man nearby to take advantage.
The midfield battle started to get tasty with tackles flying in. Mascherano was booked for flattening John Obi Mikel and soon after Cole was cautioned for a foul on Dirk Kuyt.
Torres and Riera both tested Chelsea with their direct running, but it was a very tight contest.
Michael Ballack and Frank Lampard were quick to support Nicolas Anelka, putting Jamie Carragher and Martin Skrtel under severe pressure.
After 41 minutes Riera fired in a fierce drive that was again pushed out by Cech, with Cole slicing the ball narrowly wide of the post as he cleared.
The second period was just a minute old when Alonso was cautioned for a foul on Kalou and Mikel was soon to be in referee Mike Riley's book for a foul on Alvaro Arbeloa.
Liverpool were attacking the Kop end now, and Gerrard, despite the bitter cold, was warming to his task. One run produced a corner, with Kuyt hooking wide while off balance. Then Torres saw a shot blocked by Terry.
Then on the hour Lampard was shown a straight red card for a tackle on Alonso. He connected with the ball, but also the Spaniard's ankle, and referee Riley reacted instantly.
John Terry was booked for protesting and Chelsea will rightly point out that Gerrard was only warned for a similar tackle a few minutes earlier.
Alex then deflected an Alonso drive onto the bar as Liverpool sought to claim the advantage.
On 69 minutes, Chelsea sent on Deco and Didier Drogba for Florent Malouda and Anelka.
Gerrard was booked for diving as Liverpool cranked up the pressure, with Torres having a shot hooked away by Kalou.
Benayoun then replaced Riera after 74 minutes, Liverpool searching for some invention to unlock Chelsea's rearguard. It almost came when Benayoun tested Cech from 20 yards before hooking another effort inches over.
Babel replaced Mascherano after 83 minutes and Chelsea sent on Miroslav Stoch for Kalou soon after.
And with two minutes left, Liverpool grabbed the lead with Torres' first goal in front of the Kop this season.
He arrowed a near-post header past Cech from a cross from Fabio Aurelio.
In injury-time Benayoun got away in the box after Cole failed to control and Torres fired home from eight yards.