Mason Mount’s first-half strike inflicted a fifth straight defeat at Anfield for champions Liverpool and boosted Chelsea’s top-four hopes.
The Londoners dominated the first half and thought they’d scored through Timo Werner in the 24th minute, but the goal was ruled out by VAR after an extremely tight offside call.
However, Thomas Tuchel’s side 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 ahead of another crucial game against Everton on Monday.
Meanwhile, Liverpool’s difficult season continues as Jurgen Klopp’s side, who stay seventh, go into the record books for the wrong reason after a fifth straight home defeat.