Mohamed Salah returned to haunt former club Chelsea but Liverpool were denied a hugely significant victory as Willian conjured an equaliser out of nothing at Anfield.
Salah was tried, tested and discarded with indecent haste at Stamford Bridge but has been a revelation on Merseyside, topping the Premier League scoring charts with 10 goals in 13 games after stabbing home from close range in the 65th minute.
Yet Jurgen Klopp's side were forced to settle for a 1-1 draw when substitute Willian floated the ball over Simon Mignolet in what could have been either a show of outrageous skill or sensational fortune.
Victory would have catapulted Liverpool into the top four and left Salah basking in lashings of narrative given his baffling treatment at Chelsea - but the 85th-minute leveller left them three points behind their opponents in fifth.
Both sides showed five changes from their midweek outings in the Champions League, leaving the likes of Sadio Mane, Roberto Firmino, Cesc Fabregas and Willian starting on the bench.
The alterations resulted in seven Englishmen taking the field, including Danny Drinkwater - making his first league start for Chelsea.
Liverpool pressed high and hard as they won the initial scrap for territory, but the best their early forays yielded was a Salah curler which ended up in the stands.
With Chelsea's wing-backs retreating to form a back five at times, it required more than a little craft to unlock the door. Salah was the most obvious danger, a nimble-footed menace to Marcos Alonso and Gary Cahill on the right wing, but phase after phase broke down around the box.
Chelsea were slower out of the blocks but had a clearer objective: find Eden Hazard and watch him go.
The Belgian drew the first meaningful save of the match with a rasping strike at Mignolet's near post and then teased out a glorious chance for the visitors.
Hazard's dribble pulled Liverpool out of shape and his deft pass put Drinkwater one on one with the goalkeeper. The midfielder's run was perfect but his touch was heavy, inviting Mignolet to snuff out the danger.
Salah popped up shortly before half-time, winning a yard of space from Cahill and pulling a left-footed effort just wide from the edge of the area to preserve an entertaining stalemate.
Hazard, last seen barging Philippe Coutinho off the ball firmly but fairly in the box, was quick into the game after the restart, driving his side up the field with his faultless close control.
But it was Liverpool who threatened to break the deadlock in unlikely circumstances, Sturridge flicking a dismissive effort at goal only to see Thibaut Courtois dive inexplicably over the ball as it crept wide.
Gradually, the game was breaking open at both ends - Cahill surviving a borderline penalty appeal for handball and Alvaro Morata failing to connect properly with chances at both near and far post.
Cesar Azpilicueta's selfless block denied Sturridge but an opener now seemed as inevitable as the man who scored it.
Coutinho's break had almost come to nothing when Alex Oxlade-Chamberlain stretched a boot out, making a slim but essential touch towards Salah. The Egyptian was quick to accept, prodding his shot past Courtois but declining to celebrate as he was mobbed by team-mates.
It looked to be enough to secure the points until Willian's late arrival. Whether or not he fully intended to chip the ball delicately over a crowded box and dip it just under the crossbar was not immediately apparent. What was clear was Klopp's men had allowed another winning position to escape them.
Salah went close to winning it but Courtois parried his injury-time effort wide to quash a dream day for the Reds' record signing.