PSG now have 65 points after the rescheduled week 17 match, and a game in hand over second-placed Lille on 50.
It is the first time the 20-year-old France striker, who scored PSG's final goal of the night right-footed from the left of the box in the 79th minute, has netted 20 league goals in a single season.
Full back Layvin Kurzawa had opened the scoring for the runaway leaders with a 13th-minute header but Florent Mollet equalised in the 31st for the sixth-placed visitors when he fired into the top right corner from a free kick.
Angel Di Maria made it 2-1 from another free kick on the stroke of halftime before a sudden rush of goals in a six-minute spell after the break.
Christopher Nkunku scored in the 73rd with a header off a corner and PSG went 4-1 up after an own goal by Brazilian defender Vitorino Hilton, who deflected in a shot from Mbappe.
The PSG striker made sure his name was on the scoresheet with the home side's fifth a minute later.
(Reporting by Alan Baldwin in Barcelona, editing by Ed Osmond)
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