The French champions had dominated the first half without overly troubling the Dortmund defence, but they went ahead four minutes after the break when Mbappe scored a spot-kick awarded for a Niklas Suele handball.
Achraf Hakimi added a memorable second, and PSG could have won the Group F encounter by a far more handsome margin in the end.
The result immediately puts them in control of the group, after AC Milan and Newcastle United drew 0-0 earlier, and coach Luis Enrique will hope they can build on this performance when they visit the English side next in a fortnight.
Dortmund, meanwhile, were nowhere near their best and must improve when they entertain Milan next in what is an unforgiving section.
AFP
Contact: [email protected]