Roberto Firmino scored in stoppage-time to hand Liverpool a dramatic victory.
Daniel Sturridge and James Milner had put Liverpool in a commanding position before Thomas Meunier and Kylian Mabppe hauled PSG level.
However, the Brazilian climbed off the bench to settle a pulsating contest in added time at Anfield.
Sturridge delivered a huge moment on his return to the starting line-up as he headed in Andy Robertson’s cross.
And Milner then added a second from the spot after Juan Bernat tripped Gini Wijnaldum.
But Meunier reduced the deficit as he capitalised on a Robertson error to fire past Alisson before the break.
Liverpool thought they had a third just before the hour mark but Mo Salah’s goal was ruled out after Sturridge fouled Areola.
That proved costly as Mbappe raced clear to level the scores late on, only for Firmino to win it for Liverpool at the death.
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