He had been drawing fouls from opponents and whipping up a fervent home crowd before he burst down the left in the 37th minute, combining with Mbappe.
Liverpool defender Virgil van Dijk admits he has to learn from his mistakes on a painful night in Paris.
James Milner converted Liverpool's penalty after Juan Bernat and Neymar had put PSG in control.
Liverpool are third in Group C on six points, two behind PSG and three behind Napoli, who they face at Anfield in the final round of matches on December 11.
PSG's 40-year-old goalkeeper Gianluigi Buffon had a relatively easy evening at Parc des Princes, while at the other end Liverpool's Alisson had to make saves to keep the scoreline close.
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BELGRADE, SERBIA - NOVEMBER 06: Alisson Becker of Liverpool reacts during the Group C match of the UEFA Champions League between Red Star Belgrade and Liverpool at Rajko Mitic Stadium on November 06, 2018 in Belgrade, Serbia.
He's reached the mark in just 52 Champions League games - 34 fewer than Kaka - and also has 22 assists in the competition.
PSG had only won one of their previous seven games in the competition.
"We bounced back in the second half, we did well".
FW Neymar, 8 - Shrugged off last week's injury scare to start and showed no ill-effects with a start-to-finish goal as part of an involved performance that saw his late penalty shout waved away by inept referee Szymon Marciniak and was only mildly soured by a late booking.
Atletico - whose Metropolitano Stadium hosts the final - is two points clear of Borussia Dortmund, which drew 0-0 with Club Brugge.
In Portugal, Porto and Schalke knew before kickoff they would both advance to the Round of 16.
Liverpool still need to win, but have a chance at topping the group if they win 1-0 or by a two goal cushion.