Vitinha gave PSG the lead early in the second half at the Parc des Princes before Mbappe made it 2-0 with a superb strike in off the underside of the crossbar. Matthieu Udol pulled one back for the struggling visitors but Mbappe pounced on a short backpass to round the goalkeeper and make it 3-1 towards the end.
His birthday was made even more memorable when his 16-year-old brother Ethan came on for his senior debut in stoppage time.
PSG therefore end the year with a comfortable five-point cushion over nearest challengers Nice, who defeated Lens 2-0 on Wednesday thanks to two late goals from Nigerian striker Terem Moffi.
Monaco are seven points behind the leaders in third place after coming from behind to win 2-1 at Toulouse, with Wissam Ben Yedder scoring both of their goals.
Meanwhile Lyon climbed out of the bottom three as they beat Nantes 1-0 thanks to an Alexandre Lacazette goal to claim their third consecutive victory.
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