At 20 years and 306 days old, Mbappe is almost a year younger than Lionel Messi when the Barcelona forward took the record from Raul.
The Frenchman was brought on in the 52nd minute and doubled PSG’s lead nine minutes later with a header after Simon Mignolet’s save had fallen into his path.
Mbappe latched onto Angel Di Maria’s pass for his second, before wrapping up his treble in 22 minutes when Di Maria again threaded a ball through the Brugge defense.
“I’m very happy. To come back, score three goals and get an assist, I’m really happy to have helped the team,” said the France international, who also set up Mauro Icardi’s second of the game.
“We’ve won against a tough team. At home, Brugge are a very good team. We had a great match and we’re very happy to be taking three points back home with us.”
The victory means PSG maintains a perfect Champions League record this season having defeated Real Madrid and Galatasaray in its two opening games.
Real’s 1-0 victory over Galatasary on Tuesday puts the Spanish side second in Group A, five points behind PSG.