Liverpool made it six out of six in the Premier League and re-asserted their 5 point lead at the top of this season's competition.
But this result was more about resilience and determination than a usual swashbuckling approach; LFC made to work hard in the closing stages as Chelsea chased an equaliser.
Both sides had lost their opening Champions League group game during midweek but it was the reds who made the immediate return to winning ways.
And it was Liverpool's second victory over Frank Lampard's men this season, having already won the UEFA Super Cup back in August.
The Liverpool boss, marking his 150th Premier League game at LFC, made just the one change from midweek, with the fresher legs of Gini Wijnaldum in to replace James Milner in the starting line up.
The men from Anfield started the brighter of the two teams and were easily deserving of the game's opening goal.
The imperious force of Fabinho powered through the middle before unloading a pass to Sadio Mane. Christensen sensed the danger and fouled the Senegal man just outside the box.
An indirect free kick, a touch by Mo Salah, and then a drilled effort past Kepa Arrizabalaga by the youngster Trent Alexander-Arnold.
Chelsea had to make an early substitution with Emerson heading off, but then had a brief glimpse of hope after Willian's cross stumbled across the box and Azpilicueta dispatched it into the net. However, VAR replays showed that Mason Mount had strayed offside in the build up to the goal and it was correctly chalked off.
Highlights - Chelsea 1-2 LFC
This stung Chelsea, and the reds made the most of this. Trent touching a ball to Robertson, the Scottish captain floating over a cross and Roberto Firmino rising highest to head the ball into the net. 2-0.
The second half however belonged to the blues. N'Golo Kante their particular weapon, with almost all their good play involving him, and he gave them hope midway through the half when he burst forward and fired in Chelsea's only goal of the game.
But ultimately Liverpool held their nerve and won an almost unprecedented 15th consecutive Premier League match.