In the sixth minute of extra time, Chelsea's Brazilian 18-year-old Estêvão made it 2–1.
A week ago, the reigning Premier League champion suffered its first loss of the season – 1–2 after Crystal Palace decided in the last minute.
Liverpool is second in the English top league after the losses, one point behind Arsenal. Chelsea climbed to sixth place.
Liverpool's Swedish star, Alexander Isak, was responsible for the setup for Liverpool's goal in the 63rd minute when he, turned away from the goal, elegantly brought down a cross and served the on-rushing Cody Gakpo the ball. Isak was substituted out in the 74th minute.
Moises Caicedo scored Chelsea's first goal after a quarter of an hour into the match.
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