The Reds got off to the perfect start as Trent Alexander-Arnold scored a fantastic Reds free-kick from just outside the box to give them a 1-0 lead.
Chelsea responded via a Cesar Azpilicueta goal from close-range, however, it was ruled out for offside in the build-up and the Reds soon shifted the momentum back to themselves.
With a little over 30 minutes in, a set-piece saw Andy Robertson whip the ball in to the Chelsea box, with Roberto Firmino getting on the end of it and nodding home past César Azpilicueta to double Liverpool's advantage.
N'Golo Kante scored a consolation goal for Frank Lampard's side in the second half, however, the Reds held on to make it six wins at the start of their 2019/20 league campaign.
Liverpool remain at the top of the Premier League with 18 points, leading champions Manchester City by five points after just six games.
Slide through our gallery below for all the best snaps from a successful outing for Liverpool in south west London.