Luis Enrique’s side took an early lead when Mbappé volleyed home Ousmane Dembélé’s cross to the far left of the penalty area.
Reims looked to have leveled just four minutes later when Junya Ito struck back, but the striker saw his effort ruled out for offside by VAR.
Mbappé doubled the visitors’ advantage an hour ago by pouncing from Carlos Soler’s clearance to score his 12th goal in as many top-flight games.
The France international clinched his hat-trick in the closing minutes of the match with a powerful finish after being hauled down by Bradley Barcola.
Les Parisiens have temporarily climbed to pole position in the Ligue 1 table ahead of Monaco’s trip to Le Havre on Saturday night.
PSG player ratings
GK: Gianluigi Donnarumma – 9/10 – Despite one mistake that almost proved costly, Donnarumma was superb. The Italian was often tested but was impenetrable. An inspired display.
RB: Carlos Soler – 6/10 – Struggled in the lesser-known right-back role, most of Reims’ best chances came from his side. Questionable defensively but provided a lovely assist for Mbappe.
CB: Marquinhos – 7/10 – Made a crucial save to deny Marshall Munetsi just after PSG had doubled their lead, pushing the ball away from the Reims striker as he prepared to shoot.
CB: Milan Skriniar – 7/10 – PSG’s entire backline had a tough time against Reims, especially in the first half. However, it was a mature display from the centre-back.
LB: Nordi Mukiele – 7/10 – A good battle against the impressive Ito, with both players coming out of the match with credit. Mukiele enjoyed a much easier second half.
CM: Warren Zaire-Emery – 6/10 – Some neat touches in central areas. He grew into the game after a quiet first half, although it wasn’t a particularly memorable outing for the youngster.
CM: Fabian Ruiz – 7/10 – Dictated the tempo of the game well and was characteristically comfortable in possession.
CM: Lee Kang-in – 6/10 – It wasn’t the busiest of afternoons for the South Korean as he didn’t get much involved in the proceedings.
RW: Ousmane Dembele – 7/10 – Wonderful footwork and bursts of speed, also providing a sumptuous cross for Mbappe’s opener.
ST: Goncalo Ramos – 4/10 – Anonymous during the first half and understandably hooked at halftime.
LW: Kylian Mbappe – 9/10 – A superb volley put PSG ahead early on and his spectacular drive at the far post saw him easily double his tally. He grabbed his hat-trick with time to spare in another decisive performance.