Barcelona had the better of the early stages with Keylor Navas thwarting Antoine Griezmann before Lionel Messi opened the scoring from the penalty spot after Frenkie de Jong was tripped by Layvin Kurzawa.
Paris responded emphatically as Mbappé thumped in the equaliser, and Mauricio Pochettino’s men would have led at half-time had Marc-André ter Stegen not denied Kurzawa.
The Barcelona No1 could not halt the tide, though, as Paris struck twice midway through the second half. Mbappé swept home his second after Alessandro Florenzi burst in behind the home defence, then Moise Kean headed in a Leandro Paredes free-kick to leave the visitors in a commanding position.
You sensed Mbappé would deliver the final blow and he did so five minutes from time, whipping the pick of his bunch across Ter Stegen into the top corner.