PSG seemingly wanted to move on quickly from a 3-2 home loss against Nice last time out and Lucas Hernandez almost gave the hosts a perfect antidote with a low shot inside the box that skimmed the post.
Unbeaten in four this season, Dortmund were going to provide stiff competition at Parc des Princes and the Bundesliga side eventually grew into the match and generated the first big chance when Donyell Malen wriggled into the penalty area but shot straight at Gianluigi Donnarumma.
Dortmund’s opportunity seemed to spark PSG into action as Ousmane Dembele raced down the left wing and cut back for Randal Kolo Muani to finish inside the six-yard box only for the strike to scuff his shot wide.
Sensing an opener, Les Parisiens kept the pressure on leading up to half time and almost struck first when they worked the ball patiently around Dortmund’s area before Vitinha let fly with a skidding effort that thumped the post.
PSG were relentless going forward and eventually got the breakthrough minutes after the break when Niklas Sule’s handball in the area gifted the hosts a penalty.
Without hesitation, Mbappe stepped up and caressed the ball into the bottom corner past Gregor Kobel for an 11th UCL group stage goal in his last nine appearances.
Les Parisiens quickly added a second and were well on their way to a seventh Champions League home win in nine when Vitinha played in Achraf Hakimi and the defender feinted past his marker and curled past Kobel.
Dortmund came forward with intent late on in search of a late comeback with substitute Jamie Bynoe-Gittens almost pulling a goal back with a curling strike from 20 yards that clipped the post.
A commanding PSG performance to kickstart their UCL campaign will provide Luis Enrique and his side with plenty of confidence after a tough start of just three wins from their opening six matches.
Dortmund’s travel worries rumble on in the Champions League as the German side are winless in six of their last seven on the road, so home form could be vital if Edin Terzic’s side are to progress to the knockout rounds this season.
Flashscore Man of the Match: Kylian Mbappe (Paris St Germain)