Chelsea bolstered their top four prospects as Mason Mount’s strike in the first half inflicted a fifth straight loss at Anfield for champions Liverpool.
Thomas Tuchel’s side dominated the first half and believed they had scored by Timo Werner in the 24th minute, but the goal was ruled out by VAR after an extremely tight offside appeal.
However, Chelsea’s dominance finally paid off when Mount sacked Alisson to give the visitors a deserved lead.
Liverpool showed more urgency after the break but they struggled to find their attacking mastery and failed to create many clear chances as Chelsea held on what could turn out to be a three crucial points in the Champions League qualifying race.
The victory sees Chelsea, who continue their unbeaten start to life under Tuchel, move up to fourth place ahead of another crucial game against Everton on Monday (kick-off 6pm).
Meanwhile, Liverpool’s difficult season continues as Jurgen Klopp’s side, who remains seventh, break into the record books for the wrong reason after a fifth straight loss at home.
Liverpool are back in action on Super sunday when they host Fulham, live on Sky Sports Premier League from 1pm; Kick-off at 2 p.m.
Meanwhile, Chelsea will face another top-four rival in their next game when they host Everton at Stamford Bridge on Monday; Kick-off at 6 p.m.