Both managers made two changes from their most recent Premier League outings with Roberto Firmino restored to Liverpool’s starting XI, while N’Golo Kante was handed his first appearance since August 18.
It was quite an open first 10 minutes as Chelsea and Liverpool, who recently met in the UEFA Super Cup, struggled to get a grip of the game.
But Liverpool broke the deadlock on 14 minutes courtesy of a well-worked free-kick after Sadio Mane was bundled over on the edge of the area.
Mohamed Salah rolled the ball to Trent Alexander-Arnold who smashed home emphatically into the top right corner.
Chelsea did respond well and Tammy Abraham should have levelled when he beat the offside trap, although he was denied by Adrian.
The Blues thought they had equalised just shy of the half-hour mark when Cesar Azpilicueta poked home from close range.
Their celebration was short-lived, though, after a check from VAR deemed Mason Mount had been offside in the build-up.
To add insult to injury, Liverpool pulled two goals clear just moments later when Firmino headed home Andy Robertson’s free-kick.
Injuries to Andreas Christensen and Emerson forced Lampard into two first-half substitutions and left him without much opportunity to switch things up for the second period.
They did come out fighting, however, and Kante offered hope of turning things around when he drilled beyond Adrian with around 20 minutes to play.
Substitute Michy Batshuayi and Mount had late opportunities for Chelsea but were unable to convert despite some lacklustre defending from Liverpool.
It’s just the second time that Liverpool have managed to pick up an away Premier League win in the past 13 games against established top-six opposition.
Liverpool retain their five-point lead over Manchester City at the top of the table, while Chelsea sit 11th with eight points from their opening six games.