Thomas Tuchel's side were already in front thanks to Leandro Paredes' first goal for the club when their task was made easier by Jean Eudes Aholou's 25th-minute red card.
Mbappe doubled PSG's lead and, though Neymar missed from the penalty spot, PSG did not have to get out of second gear as it extended its winning streak to five Ligue 1 games.
Mauro Icardi netted PSG's third, before Mbappe struck with the last kick of the match to add further gloss to the scoreline.
Saint-Etienne had a chance to take an early lead but Denis Bouanga curled wide, and PSG then opened the scoring in the ninth minute.
A goalmouth scramble saw the ball eventually cleared to Paredes, and his 20-yard volley took a decisive deflection off Wesley Fofana to deceive Stephane Ruffier.
The hosts were reduced to 10 men when Aholou was dismissed for a wild challenge on Paredes, and Mbappe, who earlier had a goal ruled out for offside, made it 2-0 before the break by running on to Neymar's pass to beat Ruffier.
Keylor Navas made a fine save to deny Bouanga following the restart, and Angel di Maria saw a shot come back off the woodwork.
It should have been 3-0 to PSG in the 62nd minute but Neymar hit the post from 12 yards after he was fouled in the box by Mathieu Debuchy.
Icardi converted from close range, though, the striker scoring his eighth Ligue 1 goal since joining on loan from Inter, and a fine finish from Mbappe at the death wrapped up PSG's latest win.