Mohamed Salah’s 65th-minute goal against his former side had looked to have given the Reds all three points, but Willian’s chip – which appeared to be a cross – looped over Simon Mignolet and into the goal with five minutes of the clash remaining on Saturday evening.
The draw keeps Chelsea in third place in the Premier League standings, three points behind Manchester United, while Liverpool are in fifth, a point off fourth-placed Tottenham.
After overseeing a 4-0 win away to Qarabag in the Champions League on Wednesday, Conte opted to not start David Luiz – who performed solidly in Baku – at Anfield and instead play Andreas Christensen.
The Italian also decided to hand Danny Drinkwater his first Premier League start of the season as the England international slotted into a more defensive-looking midfield alongside N’Golo Kante and Tiemoue Bakayoko.
While these changes were not so much a surprise, what was a surprise was Jurgen Klopp putting Sadio Mane and Roberto Firmino on the bench for the hosts and starting Alex Oxlade-Chamberlain and Daniel Sturridge.
The changes did, however, appear to work for the Reds in the early stages of the game, with Oxlade-Chamberlain getting the better of Davide Zappacosta with his pace on the left while former Chelsea winger Salah caused Marcos Alonso all sorts of problems on the other flank.
But for all of Liverpool’s early dominance, the hosts began to get sloppy as they gave the ball away on a few occasions which allowed Chelsea to start testing Mignolet.
First the Belgian was forced into parrying clear Eden Hazard’s low shot before he rushed out to superbly collect the ball from the feet of the incoming Drinkwater and then punched clear Zappacosta’s fierce, long-range shot.
Those chances marked a turning of the tide at Anfield for a while, with Chelsea really unsettling Liverpool.
Klopp’s men recovered, however, and could have scored when Salah – who had netted nine Premier League goals coming into the game – got past Gary Cahill and Kante to drive a low shot wide of the far post in the 40th minute.
The Anfield fans were then left screaming for a penalty kick after Philippe Coutinho went down in the box under pressure from Hazard. Nothing was – rightly – given and the score-lined remained goalless at the break.
The hosts returned in the second half seemingly intent on finding the opener but found Chelsea defensively stubborn to break down, demonstrated when Cesar Azpilicueta’s last-ditch body block denied Sturridge from inside the box.
Yet, Liverpool did eventually take the lead – and it came through former Chelsea winger Salah.
Coutinho did much of the hard work to create the opener and, after sending the ball toward Salah, Bakayoko’s touch inadvertently moved it into the path of Oxlade-Chamberlain.
The winger poked it forward to Salah, who coolly slotted the ball past Thibaut Courtois to hand the hosts the lead in the 65th minute.
The hosts looked to be cruising to a victory but, when Conte brought on a host of changes – including Willian – the Blues found the equaliser they were looking for.
The Brazilian, who scored twice and won two penalties against Qarabag, sent a chip toward the far post in the 85th minute but instead saw the ball fly over Mignolet and into the goal.
Courtois was needed to thwart Salah from close range at the death, but Chelsea held on to extend their unbeaten run at Anfield to six league games.