Mbappé's first came soon after Martin Terrier had given Lyon the advantage in the 11th minute.
The 21-year-old France international was also instrumental in PSG taking the lead in the 64th minute from the penalty spot.
Collecting the ball out on the left wing, he surged past two Lyon defenders before floating over a cross to Edinson Cavani, who controlled the ball only for Fernando Marcal to handle before the veteran striker could shoot.
Neymar slotted home the subsequent spot-kick while Marcal was sent off for a second yellow card.
Surge
Trailing, and numerically disadvantaged, Lyon went further behind in the 70th minute.
After picking up the ball in his own half, Mbappé burned past Lyon midfielder Bruno Guimaraes and held off defender Marcelo before firing past Lyon goalkeeper Anthony Lopes.
Pablo Sarabia added the gloss in the 81st minute before Mbappé completed his hat trick in stoppage time.
Streak
The five goal mauling ended Lyon's five-match unbeaten run that included an impressive 1-0 win over Juventus in the first leg of their last 16 Champions League tie and last weekend's Ligue 1 triumph over local rivals Saint-Etienne.
"When you are 10 against 11 playing such a strong team it's no longer a contest," said Lyon boss Rudi Garcia. "But for the hour before the red card, we were causing PSG lots of problems."
Revenge
While Lyon lick their wounds, they have the chance to avenge the thrashing next month when they take on PSG in the final of the League Cup.
PSG, who have hoisted that trophy five times in the last six seasons, continue their pursuit of a domestic treble.
They will face Saint-Etienne or holders Rennes in the Coupe de France final and they are 13 points clear in Ligue 1 with 11 games remaining.
"It was a solid, serious display full of concentration," said PSG coach Thomas Tuchel. "We were worth the win and it's a fantastic result. Five goals at Lyon is extraordinary."
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