Second-half substitute Estevao scored a dramatic late winner to inflict a third consecutive defeat on Liverpool.
The reigning Premier League champions have now dropped to second in the table, behind new leaders Arsenal.
Chelsea started brightly and took the lead through a fine finish from Moises Caicedo.
Cody Gakpo looked to have secured Liverpool a hard-fought point, only for 18-year-old Estevao to score in the 96th minute and snatch the victory.
Chelsea return to action after the international break with a trip to Nottingham Forest, while Liverpool will look to get back to winning ways with the visit of Manchester United.
These two teams will not play for another fortnight as the domestic action breaks away for the second international break of the season.
Two big games when they return; Chelsea are away to Nottingham Forest in exactly two weeks’ time before Liverpool host Manchester United a day later.
Then they are straight back in Champions League action, both on October 22 — Chelsea host Ajax and Liverpool have a trip to Frankfurt to navigate.
THEATHLETIC
