Frank Lampard's men failed to contain the European champions, who benefited from two first-half injuries to a Chelsea defense 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
TRENT! pic.twitter.com/DIsM6YRBjs— NBC Sports Soccer (@NBCSportsSoccer) September 22, 2019
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.
Roberto Firmino climbs the ladder! 🔥⚽️— NBC Sports Soccer (@NBCSportsSoccer) September 22, 2019
2-0 Liverpool! 🔴 pic.twitter.com/NE3zq4ZhtF
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.
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.
Ngolo Oh!— NBC Sports Soccer (@NBCSportsSoccer) September 22, 2019
Ngolo Oh! pic.twitter.com/Z2FQfkPD2c
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.
13 - Chelsea have conceded 13 goals in their opening six Premier League games for the first time, last conceding as many in the top-flight in 1978-79 (also 13) - a season in which they finished bottom of the First Division. Brittle. pic.twitter.com/2GSIC5O3QH— OptaJoe (@OptaJoe) September 22, 2019
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 defense
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.
After a trip to Milton Keynes Dons in the EFL Cup, Liverpool return to Premier League action at Sheffield United, while Chelsea head into home games against Grimsby Town and Brighton and Hove Albion.