PSG had the better of the early exchanges but it was Barca who struck first before the half-hour mark.
Frenkie de Jong was awarded a penalty in the 27th minute when Layvin Kurzawa accidentally clipped his trailing foot while running to reach a long ball behind the PSG defence. Lionel Messi stepped up and confidently beat keeper Keylor Navas to put Barca ahead.
Mbappe quickly answered minutes later with an expert finish following a flowing team move. The France international settled a cushioned Marco Verratti chip, used some neat footwork to wriggle free of defenders and fired into the roof of Marc-Andre ter Stegen‘s goal from close range.
Mbappe put PSG in front in the 66th minute when he pounced onto a deflected low cross and placed his shot into the empty net with Ter Stegen out of the way.
PSG took firm command of the tie four minutes later from a Leandro Paredes free kick on the left. Moise Kean headed down and past Ter Stegen after being left alone at the back post by a slack Barca defence.
Mbappe completed his hat trick five minutes from time with a sumptuous curled finish to cap a counter-attack, giving Barca a sizable mountain to climb in the second leg in Paris on March 10.