Liverpool were pushed all the way by Chelsea at Stamford Bridge, and had to hang on in the end to make it six wins in a row with a 2-1 success.
Trent Alexander-Arnold and Roberto Firmino grabbed the first half goals, either side of Chelsea having a goal ruled out by VAR, before the excellent N'Golo Kante pulled one back in the second half to set up a frantic finish.
Liverpool missed chances to kill the game off, while Chelsea missed a couple of opportunities to secure a point in what was a fascinating contest - with Frank Lampard's men finishing the stronger and forcing the European champions to hang on in the end.
Jurgen Klopp's side restored their five-point lead at the top of the Premier League after a sixth straight win of the season, and 15th overall in their magnificent run, while Chelsea were applauded off by the home crowd after putting up a hugely promising performance - especially the magnificent Kante in his first game back from injury.
After a lively start from both sides, Alexander-Arnold gave Liverpool the lead on 14 minutes with a piece of quick-thinking was followed by a ferocious shot that flew into the top corner.
Match highlights
Mohamed Salah shaped up to take the free kick just outside the box, but instead back-heeled the ball to the Reds right back who lashed his shot beyond the helpless Kepa.
Chelsea looked to have levelled through skipper Cesar Azpilicueta after some pinball in the Liverpool box, but it was chalked off by the VAR as mason Mount was narrowly offside in the build-up.
The anger of the Chelsea fans intensified just three minutes let when Firmino doubled Liverpool's lead when he had a free header to nod in Andy Robertson's cross.
Liverpool came out quicker in the second half and had a couple of chances to kill the game off through Salah, while Firmino had a back-post volley superbly turned away by Kepa.
Adrian also made a good save at the other end, but could do nothing about Kante's brilliant effort, as the midfielder went on a scamper right through the heart of Liverpool's defence before firing an unstoppable effort right into the top corner.
Mount missed a glorious chance late on as Chelsea pushed for an equaliser, but Liverpool managed to hold on to make it six wins out of six and 15 Premier League wins in a row for Klopp's side.
Chelsea 1-2 Liverpool Opta stats
- Liverpool are the first team in top-flight history to win their opening six matches of a top-flight season in two consecutive seasons.
- Chelsea have conceded 13 goals in their six Premier League matches this season – their most after six league matches of a season since 1978-79 (also 13), when they went on to finish bottom of the First Division.
- Liverpool have won consecutive Premier League matches against Chelsea for the first time since a run of four wins between November 2010 and May 2012.
- Liverpool have won their last 15 league matches – the only team with a longer winning run in top-flight history is Manchester City (18 between August and December 2017).
- Chelsea have lost consecutive home matches in all competitions for the first time since April 2014, when they lost against Sunderland and Atlético Madrid.
- Jürgen Klopp managed his 150th Premier League game today – he has registered 92 wins in those games, with only José Mourinho (105) winning more in his first 150 matches in the competition.
- Frank Lampard is only the second Chelsea manager to fail to win any of his first four home matches in all competitions (W0 D2 L2), after Bobby Campbell in 1988.
- Since the start of the 2018-19 season, Liverpool have scored 34 goals from set-piece situations in the Premier League – seven more than any other team.
- Chelsea have failed to win any of their opening three home Premier League matches in a season for only the second time, also doing so in 2001-02 during Frank Lampard’s first season there as a player.