The 22-year-old France striker’s efforts either side of the break saw him become the youngest player to score 100 goals in the French top flight.
Mbappe opened the scoring from a tight angle, before Danilo Pereira made it 2-0 with a half-volley and Angel di Maria added a third early in the second half.
Mbappe netted again before Islam Slimani and Maxwel Cornet responded.
Victory lifts PSG to the summit on goal difference above Lille, who were beaten 2-1 at home by Nimes earlier on Sunday.
Mbappe replaces Herve Revelli, who achieved the feat with Saint Etienne in 1969, as the youngest player ever to score 100 goals in the French top flight.
Victory against third-placed Lyon also saw Brazilian forward Neymar return from a six-week injury layoff, coming off the bench to replace Mbappe in the 70th minute.