Neymar was also on target as PSG secured a ninth Ligue 1 success in a row from the start of the season, eclipsing the 82-year-old record set by Olympique Lillois during the 1936-37 campaign.
A scrappy first half, which saw red cards for PSG defender Presnel Kimpembe and Lyon midfielder Lucas Tousart, turned into the Mbappe show as the forward claimed his first hat-trick for the champions.
Mbappe scored four times between the 61st and 74th minutes as Lyon, unbeaten in their previous six games, were unable to stop the rampant 19-year-old.
Lyon suffered a nightmare opening with Nabil Fekir limping off in the seventh minute after failing to run off a foot injury sustained in a Thiago Silva tackle.
PSG were ahead moments later when Mbappe was scythed down after Lyon goalkeeper Anthony Lopes suffered a rush of blood and stupidly raced from his goal.
Neymar nonchantly rolled the penalty home for his 11th goal of the season and his seventh in the last four games.
Lyon responded well as Tanguy Ndombele scuffed his shot when well placed and Memphis Depay's dipping 30-yard free-kick forced Gianluigi Buffon to tip over.
They also saw appeals for a penalty waved away when Angel Di Maria handled at a corner.
PSG were reduced to 10 men after 32 minutes with Kimpembe's lunge catching Ndombele high on the shin.
Kimpembe was initially shown a yellow card, but the severity of the challenge was highlighted on video assistant referee review and the defender was correctly dismissed.
Edinson Cavani was sacrificed as part of a PSG reshuffle and Lyon would have been level but for the unmarked Jason Denayer making a mess of a Depay free-kick.
The contest became a 10-a-side affair right on half-time when Tousart needlessly tripped Mbappe to earn a second yellow card.
It was Tousart's second dismissal in three games and let PSG off the hook when the Parisians appeared to be creaking.
Lyon substitute Maxwel Cornet nearly scored twice after the re-start, first failing to take advantage from close range and then inadvertently heading against a post when Thiago kicked the ball straight at him.
But the night belonged to Mbappe after he had hit the woodwork and twice forced Lopes into full-length saves.
Mbappe's first goal went off both posts, his second was a simple tap-in and the next two showed the ruthless quality of his finishing with Neymar heavily involved on each occasion.
Lyon refused to throw in the towel and Depay hit the crossbar with a delicious chip that Buffon managed to get the faintest of touches on.
Neymar almost had the final word with an audacious overhead kick which just cleared the Lyon crossbar.