Mohamed Salah appeared set to punish his former club when he broke the deadlock in an absorbing contest after 65 minutes.
But Brazil international Willian, who scored twice in the 4-0 Champions League win over Qarabag in midweek, picked out the far corner with a chipped attempt from the right-hand side of the penalty area five minutes from time – Liverpool goalkeeper Simon Mignolet caught out as he shaped to cross.
Roaming behind Chelsea striker Alvaro Morata, Eden Hazard was the game's outstanding player during the opening 45 minutes, while Salah relished providing Liverpool's sharpest attacking threat after Jurgen Klopp surprisingly opted to bench Sadio Mane and Roberto Firmino following the midweek collapse at Sevilla.
Egypt star Salah scored twice in 13 Premier League games for Chelsea before being farmed out to Fiorentina and Roma in Serie A but now has 10 in as many top-fight appearances since swapping the Italian capital for Merseyside during the close season.
Yet, the final word came from Willian, with boss Antonio Conte tearing jubilantly around on the touchline. His champions are three points behind Manchester United in third, with Liverpool two places and three points further back.
144 - Willian scored just 144 seconds after coming on as a substitute - the fastest in the Premier League this season. Lob.— OptaJoe (@OptaJoe) November 25, 2017
Daniel Sturridge led the line for Liverpool and held up play tidily to tee up Salah after 10 minutes – the in-form winger firing a speculative attempt off target.
Liverpool were on top without creating any clear openings during the opening 20 minutes, while Hazard was predictably to the fore when Chelsea first threatened.
The Belgium forward brought down Danny Drinkwater's lofted pass on the left and cut infield, forcing countryman Mignolet to push a well-hit drive behind.
Roles were reversed in the 24th minute as Hazard panicked the Liverpool defence with a purring run and threaded a pass through to Drinkwater.
Mignolet stuck out a well-judged boot to deny the former Leicester City midfielder before parrying from Davide Zappacosta – Hazard was the provider once more – and observing a frantic penalty box scramble from the resulting corner.
Chelsea wing-back Marcos Alonso saw his 32nd-minute free-kick curl wide, while not for the first time Salah got the better of Gary Cahill and landed a shot narrowly beyond the post with Thibaut Courtois beaten.
A rare error from Courtois almost gave Liverpool the lead four minutes into the second half when Sturridge's clipped shot squirmed through his grasp and perilously close to the far corner.
Again Chelsea were on the back foot and again Hazard roused them, orchestrating a lightning 60th-minute attack that ended with a vital sliding interception from Joe Gomez to prevent Morata from converting Zappacosta's low centre at the back post.
Cesar Azpilicueta blocked bravely from Sturridge after the England international's fledgling link-up with Salah showed further promise and it was the Egypt winger who found the 65th-minute breakthrough.
Tiemoue Bakayoko botched what should have been a routine clearance, allowing Alex Oxlade-Chamberlain to prod the ball into Salah's path for him to slide a cool finish past the advancing Courtois.
goals for the Reds... pic.twitter.com/M2fk5Hgh9B— Liverpool FC (@LFC) November 25, 2017
With Hazard's influence on the wane, Chelsea appeared to be struggling to muster a response when Cahill blocked bravely from substitute Georginio Wijnaldum in the 78th minute.
However, Willian – one of the men indirectly responsible for Salah's truncated Stamford Bridge career – hauled them level.
Salah is set to remain the toast of Anfield regardless, on account of racing to 15 goals in all competitions, and Courtois needed sharp reactions to deny him from James Milner's knockdown in stoppage time.
Key Opta stats:
- The Reds are unbeaten in their last six Premier League games against Chelsea (W2 D4) – their joint-longest ever such run against them in the competition (also six between March 1994-September 1996 and November 2010-April 2013).
- However, they’ve not beaten them in the Premier League at Anfield since a 4-1 win in May 2012.
- Liverpool have conceded just two goals in their last nine Premier League games at Anfield, but these goals have cost them a total of four points (1-1 vs Burnley, 1-1 vs Chelsea).
- Of the 19 sides Antonio Conte has faced in the Premier League as a manager, Liverpool are the only side he has not beaten in the competition.
- Mohamed Salah scored his 10th league goal for Liverpool in his 13th game for them – no player scored more in their first 13 Premier League apps for the club (level with Daniel Sturridge).
- Salah also became the 20th different player to score a Premier League goal against Chelsea having previously appeared for the Blues in the competition.
- Since Jurgen Klopp joined in October 2015, Liverpool have won 38 Premier League points in fixtures between the ‘big six’ – six more than any of the other sides (Chelsea, 32).
- In fact, Klopp is only the fourth Liverpool manager to remain unbeaten in his first five top-flight clashes against Chelsea – the others are David Ashworth, Kenny Dalglish and Roy Evans.