Without the suspended Neymar, PSG relied on Mbappe in Paris and the former Monaco prodigy delivered with an assist for Mauro Icardi's opener before rounding off the win himself late on.
Trailing from the 19th minute, Monaco huffed and puffed, but the closest Niko Kovac's team came to an equaliser was when Gelson Martins' deflected cross clipped the crossbar.
Monaco's defeat in their first appearance in a Coupe de France final in 11 years was sealed with nine minutes remaining, Mbappe dinking home to seal PSG's 14th triumph in the competition.
Neymar may have been missing for Mauricio Pochettino's side, but PSG's other key man was at the heart of their opener.
Having pounced on Axel Disasi's heavy touch following a goal-kick, Mbappe kept his cool to tee up Icardi for a simple finish into an empty net.
Alessandro Florenzi drew a save out of Radoslaw Majecki as PSG pressed for a second, though Keylor Navas had to smother Kevin Volland's header at the other end.
Wissam Ben Yedder will be at Euro 2020 after another excellent season, but the France forward – and Monaco's talisman – was replaced after an hour without having registered a shot as PSG continued to keep Kovac's men at arm's length.
Fortune was on PSG's side with 20 minutes remaining – Gelson's cross, which took a deflection, hitting the woodwork after looping over Navas.
Krepin Diatta snatched at an effort from inside the area, though Monaco looked short of ideas, and moments after striking the bar with a long-range chip, Mbappe made sure of the win when he raced onto Angel Di Maria's pass and lofted in a neat finish.