Chelsea boosted their top-four hopes as Mason Mount’s first-half strike inflicted a fifth straight defeat at Anfield for champions Liverpool.
Thomas Tuchel’s side dominated the first half and thought they had scored through Timo Werner in the 24th minute, but the goal was ruled out by VAR after an extremely tight offside call.
However, Chelsea’s dominance did eventually pay off when Mount fired past Alisson to give the visitors a deserved lead.
Liverpool showed more urgency after the break, but they struggled to find their fluency in attack and failed to create many clear-cut chances as Chelsea held on for what could prove to be a crucial three points in the race for Champions League qualification.
Victory sees Chelsea, who continue their unbeaten start to life under Tuchel, move up to fourth in the Premier League table ahead of another crucial game at home to Everton on Monday (kick-off 6pm).
Meanwhile, Liverpool’s difficult season continues as Jurgen Klopp’s side, who stay seventh – four points behind Chelsea – go into the record books for the wrong reason after a fifth straight home defeat.
Chelsea enjoyed the better of opening exchanges and they created the first real opening as Werner beat the offside trap, but he couldn’t lift the ball over Alisson, who made a comfortable save.
Tuchel said before the game they would be looking to exploit Liverpool’s high line with Werner’s pace, and they thought the plan had paid off when Werner once again raced in behind the home defence to latch onto Jorginho’s pass.