The Parisians took the lead in the second minute at Parce des Princes thanks to Dani Alves, and went on to storm ahead via goals from Edinson Cavani and Neymar.
Mbappe, who assisted Cavani’s strike, was delighted to claim a win against Die Roten but remains determined to keep the wins coming.
“It’s just the beginning of a great adventure. We really wanted to pull out a big game tonight against a formidable opponent. Mission accomplished.
“There was a lot of expectation and we played a really good game. We had a game plan, but against teams of this calibre, you have to be able to adapt.
“With our squad, we can play a possession-based game, but also win games on the counter-attack, like tonight. We will try to maintain this form and keep on winning.”
PSG are at the top of Group B after beating Celtic and Bayern in their opening two games of the Champions League group stage.