Andreas Christensen was sent off in first-half injury time for hauling down Mane as he raced onto a sublime ball from Jordan Henderson, prompting a swift collapse from Frank Lampard’s side.
Mane broke the deadlock five minutes after the restart when he headed home Roberto Firmino’s cross, after an incisive one-two between the Brazilian and Mohamed Salah had carved Chelsea open.
The winger doubled Liverpool’s lead just four minutes later when he was rewarded for closing down Kepa Arrizabalaga. Mane intercepted the Spaniard’s attempt to play the ball out before coolly tucking home from close range.
At the other end, Alisson spared Reds debutant Thiago Alcantara’s blushes when he denied Jorginho from the penalty spot in the 75th minute, after the Spaniard had clipped Timo Werner’s heels.
The Blues secured a top-four finish last season but shipped 54 goals in the process, the worst defensive record in the Premier League’s top half.
Although the Reds largely dominated proceedings in the first half on Sunday, they hadn’t caused Chelsea too many problems until Christensen’s dismissal, which proved another costly lapse at the back for them under Lampard.
Another recurring theme of Chelsea’s struggles last season was Kepa, whom the Blues made the most expensive goalkeeper in the world in 2018. He added another high-profile error to his increasing reel of mistakes between the sticks when he failed to clear his lines for Mane’s second goal.
The Spaniard had already produced a nervy moment at the back in the 14th minute when he flew off his line to reach the ball out wide, only for Salah to get there first and cross the ball to Firmino. If not for a timely block by Christensen, the Brazilian would have turned the ball into an empty net.
Chelsea have now lost four consecutive Premier League games to Liverpool, who finished 33 points ahead of them last season.
While there were some encouraging flashes from Werner and Kai Havertz at the other end, the Blues’ continued vulnerability at the back shows the scale of the challenge they face in making up the gulf between themselves and the reigning champions.
Chelsea still have new arrivals Ben Chilwell, Thiago Silva to incorporate into their backline, as well as winger Hakim Ziyech, and according to reports have already agreed a £22 million ($28 million) deal to sign Rennes goalkeeper Edouard Mendy.
Lampard will be hoping the new recruits can shore up their leaky defense, and they’ll need them to if the Blues are to have any hope of providing a serious challenge to Liverpool and Manchester City for the title.