Mason Mount gave Chelsea a crucial victory in the race for the Champions League as his strike condemned Liverpool to a fifth-straight home league defeat for the first time in their history.
The Blues were the more dangerous side from the start, with Timo Werner twice going close early on and then having a goal overturned for offside after a Video Assistant Referee review.
Instead, it was Mount who gave Chelsea their deserved lead in the 42nd minute, cutting inside from the left corner of the box and whipping a clinical finish into the bottom right corner.
The visitors continued to threaten after the break, with Ben Chilwell forcing a save from Alisson and Hakim Ziyech’s follow-up being blocked on the line by Andrew Robertson.
Liverpool’s Diogo Jota made his return from injury after a three-month lay-off, but the Reds finished the match with just one attempt on target, while it took another Alisson save to stop Werner making it 2-0.
Chelsea, who are unbeaten in their 10 matches under Thomas Tuchel in all competitions, climb to fourth.
Liverpool drop to seventh, having been overtaken by Merseyside rivals Everton.