Liverpool star Philippe Coutinho scored an equalising goal on the stroke of half time to cancel out Ramires's fourth-minute header for Chelsea at Stamford Bridge.
The defending Premier League champions, who have only won three league games this season, have experienced more misery after relinquishing a one-goal lead.
The West London outfit opened the scoring when Cesar Azpilicueta managed to shake off James Milner before driving towards the byline.
The Spaniard swung in the cross, and after the ball took a slight deflection, Ramires was well placed to head the ball down into Simon Mignolet's right bottom corner.
Liverpool were shaken and could have been 2-0 down inside eight minutes after John Terry headed Willian's 30-yard set-piece delivery across the face of goal, but Kurt Zouma could not take a touch to nudge the ball into the net.
Fortunately for Liverpool, had the ball gone in, the goal would have been ruled offside, but it was not much consolation for the Reds as Chelsea orchestrated the opening stages of the game.
Asmir Begovic was called into action for the first time when Nathaniel Clyne charged towards the byline to send in a low cross, but the Chelsea goalkeeper dropped down at his near post to prevent a red shirt from latching on to the ball.
The visitors were caught out at times as Chelsea found acres of space, particularly on the counter-attack, but Liverpool showed signs of high pressing and glimpses of attacking presence on goal.
However, without a target man, Jurgen Klopp's men struggled to trouble Begovic inside the first 15 minutes.
Liverpool settled into the game after a spell of possession and Adam Lallana attempted to level things up when he powered a shot on the turn, running away from goal, but Begovic saved comfortably.
Despite storming to a 1-0 lead, Chelsea dropped off slightly as they had to soak up some pressure from their opponents, but Begovic was relatively comfortable as every attack on his goal resulted in a simple save.
A needless challenge from Emre Can, who avoided a booking, on Willian gave Chelsea a free kick on the right side of the area, but the Brazilian's delivery failed to beat the first man and the chance was gone.
In the 34th minute, Clyne and his manager Klopp screamed for a hand ball after the full-back's kick towards the box grazed Terry's arm, but referee Mark Clattenburg waved away their claims, despite the Chelsea skipper's arms being raised.
Lucas found himself in an unfamiliar position in the box as Milner whipped in a delivery, and despite rising above Zouma to get the header on, Begovic once again made a comfortable save.
After large spells of domination, Liverpool eventually found the breakthrough two minutes into added time when Coutinho picked up the ball on the edge of the area before cutting past Ramires and curling his effort into the back of the net.
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