Frank Lampard's men failed to contain the European champions, who benefited from two first-half injuries to a Chelsea defence that never looked comfortable.
Trent Alexander-Arnold scored a thunderbolt before Roberto Firmino rose unmarked to double Liverpool's lead and there was no way back for Chelsea, despite N'Golo Kante's sensational solo effort preceding a late rally.
Injuries to Emerson Palmieri and Andreas Christensen compounded Lampard's woes, while opposite number Jurgen Klopp enjoyed a problem-free afternoon as he became the first Liverpool manager to win three times at Stamford Bridge in the Premier League.
Willian had a penalty appeal turned down after seven minutes when Virgil van Dijk appeared to bundle him over without touching the ball.
The referee blew his whistle without hesitation when Christensen brought down Sadio Mane and Mohamed Salah used the free-kick to tee up Alexander-Arnold for a thunderous 20-yard shot into the top right corner.
Cesar Azpilicueta thought he had equalised from close-range 12 minutes later but his effort was ruled out for offside and Liverpool promptly doubled their lead, Andy Robertson's curling free-kick finding Firmino to head home.
Chelsea, who had already lost Emerson to a thigh injury, saw Christensen limp off with a knee problem to cap a torrid first half, but Kepa prevented further misery for Lampard when he saved well from Firmino after the interval.
Like @nglkante, this goal is just beautiful. He weaves his way through the Liverpool defence and strokes it into the top corner from the edge of the box!— Chelsea FC (@ChelseaFC) September 22, 2019
1-2 [71'] #CHELIV pic.twitter.com/2O2ptAFTqD
With Tammy Abraham misfiring, the hosts' most potent attacking threat came from Kante who weaved his way to the edge of the box before scoring with a deft finish after 71 minutes.
Abraham's replacement Michy Batshuayi and Mason Mount both missed glaring late chances as a miserable afternoon for Chelsea ended with groans around Stamford Bridge.
What does it mean? A gulf in class
Less than 18 months ago, Liverpool lost 1-0 to Chelsea at Stamford Bridge and finished just five points above them in the 2017-18 Premier League table.
The Blues look unlikely to get anywhere near as close to catching Liverpool this season, especially with their resources so stretched and transfers unavailable to them.
Fab protects Reds' back four
Fabinho bossed the first 45 minutes of this game, driving the visitors forward and providing Liverpool's defence with steely protection.
Alonso at fault in patchwork defence
Chelsea were on the cusp of getting back into the contest when Alonso let Firmino roam free in the box, the Brazil international taking full advantage of the loose marking as he put the Reds 2-0 up.
Key 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 lost consecutive home matches in all competitions for the first time since April 2014, when they lost against Sunderland and Atletico Madrid.
- Jurgen Klopp managed his 150th Premier League game today – he has registered 92 wins in those games, with only Jose 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.