A goalless first half ended with Christensen sent off for a rugby tackle that prevented the Liverpool forward run clean through on goal – the referee initially gave a yellow card, before a pitchside VAR check saw him upgrade the punishment.
Liverpool wasted precious little time making their extra man count after the break, as debutant Thiago, on as a half-time substitute helped create that move that saw Mane head in Roberto Firmino’s cross right-wing cross.
Moments later the Senegal international charged down a clearance from Chelsea keeper Kepa and hammered in the loose ball.
Chelsea did have a chance to get back into the game with 15 minutes to play when Timo Werner was tripped in the box by Thiago, but Jorginho’s tame penalty was easily saved by Alisson.
Frank Lampard has spent more than £200million on his summer overhaul, but Chelsea’s porous defence still endures.
Kepa commanded a world-record £72million fee for a goalkeeper in 2018 but has never lived up to that price-tag, with this latest error potentially his last in Chelsea colours for some time.
The 25-year-old dallied inexplicably on the ball under grave pressure from Mane and paid the ultimate price, as the Liverpool forward blocked his clearance and tapped into the empty net.
Rennes goalkeeper Edouard Mendy is expected to complete his Chelsea move shortly, and the extra competition between the sticks cannot arrive soon enough.
Mane’s opener had arrived just four minutes earlier, as the 28-year-old nodded home Roberto Firmino’s fine cross.
Chelsea kept shape and threatened several times for the bulk of an engaging first half – but then Christensen’s fully deserved red card changed the game.
The Denmark international rugby tackled the goal-bound Mane, just as he was bracing to chip a stranded Kepa.
A stunned Jurgen Klopp turned to his Liverpool replacements and offered an immediate assessment of Christensen’s agricultural challenge, bellowing: “Are you crazy? We never, ever do that, OK?”
Chelsea will hope Brazil stalwart Thiago Silva can firm up their defence once the Paris St Germain recruit finds match fitness, but this was a chastening loss even though the red card proved pivotal.
Chelsea’s robust midfield of N’Golo Kante, Jorginho and Mateo Kovacic offered much-needed solidity and shape, while Kai Havertz ghosted around the central areas to allow Timo Werner to cut in from the left.
Werner received a major reprieve when dragging wide with the goal at his mercy, with the offside flag lifting his embarrassment.
Mohamed Salah drilled a smart low ball right across the face of goal as Liverpool threatened too, but with no team-mates driving into the six-yard box the chance went begging.
Kovacic’s lofted pass begged for a finish, but Mason Mount could not reach the teasing chipped ball, and the opportunity vanished.
Just as a cagey half looked to be heading for a humdrum conclusion though, Mane tore in off the left and caught Christensen napping.
Christensen hauled down the escaping Mane, who had the beating of the onrushing Kepa – and, eventually, was given his marching orders.
Referee Paul Tierney initially dished out a booking, but a VAR check quickly concluded the only decision, that Christensen had to go.
Lampard sacrificed Havertz at the break, bringing on Fikayo Tomori to replace Christensen, while Thiago made his Liverpool debut after Jordan Henderson suffered a thigh issue.
Liverpool wasted precious little time making their extra man count after the break, with Mane heading in after a neat exchange between Firmino and Salah.
And then came Kepa’s latest Blues aberration, leaving Mane to add a second.
Chelsea kept battling even though the game was gone, with Werner impressing to win a smart penalty.
Jorginho’s miss summed up Chelsea’s day though, with his previously rock-solid spot-kick technique picked apart by Alisson’s fine save.