Estevao Willian struck deep into stoppage time to give Chelsea victory and condemn Liverpool to a third successive defeat in a dramatic climax at Stamford Bridge.
Chelsea's winning goal, greeted with wild celebrations that ended with coach Enzo Maresca being sent off, was deserved but it was another bitterly disappointing outcome for the out-of-sorts Premier League champions.
Moises Caicedo made the breakthrough for the hosts after 14 minutes as he fired a rising 20-yard drive past Giorgi Mamardashvili, deputising for the injured Alisson.
Liverpool head coach Arne Slot dropped £116m summer signing Florian Wirtz to the bench after losses at Crystal Palace and Galatasaray, but he was introduced at the start of the second half in an attempt to provide some inspiration.
Chelsea remained in control, but Liverpool's equaliser came after 62 minutes, Cody Gakpo reacting quickly in the six-yard area to beat Robert Sanchez after Alexander Isak had touched on Dominik Szoboszlai's cross.
Liverpool keeper Mamardashvili made two important late stops from Estevao and Jamie Gittens, while Enzo Fernandez wasted a golden opportunity to give Chelsea victory in added time, heading against the outside of the post with the goal at his mercy.
It looked like the last act until Liverpool were undone in the dying seconds - as they were at Crystal Palace - with Estevao stealing in front of Andrew Robertson to turn Marc Cucurella's cross past Mamardashvili.
The result leaves Arsenal top of the table - a point ahead of Liverpool - after they beat West Ham United earlier on Saturday.