Chelsea held on after a first-half red card to draw 1-1 and deny Liverpool a win that would have taken them top of the Premier League.
Kai Havertz's looping header from Reece James' corner gave Chelsea the lead on 22 minutes.
But the match turned in the third minute of first-half stoppage time, when James handled Sadio Mane’s close-range shot on the goalline.
The Chelsea defender was sent off and Mohamed Salah converted the resulting penalty for his 99th Premier League goal.
Liverpool applied pressure in the second half, with Edouard Mendy denying Virgil van Dijk, Fabinho and Andrew Robertson among six saves he made.
Chelsea looked to stun Liverpool on rare breaks and the closest they came was when Romelu Lukaku's close-range shot was blocked by Joel Matip.
Both teams have seven points, with Chelsea in second, one place above Liverpool.
Liverpool: 12 Sep v Leeds (A)
Chelsea: 11 Sep v Aston Villa (H)
Referee: Anthony Taylor. Assistants: Gary Beswick, Adam Nunn. Fourth official: Craig Pawson. VAR: Chris Kavanagh. Assistant VAR: Sian Massey-Ellis.