Vitinha put PSG ahead at the Stade de la Mosson and Mbappe doubled their advantage midway through the first half, only for an Arnaud Nordin header and a Teji Savanier penalty to bring Montpellier back level at the interval.
However, a marvellous Mbappe goal restored PSG’s lead shortly after the break and Lee Kang-in made it 4-2 before the France captain completed his hat-trick.
Nuno Mendes put the seal on the victory late on, as Luis Enrique’s side ended a run of three successive draws in Ligue 1 and extended an unbeaten domestic record stretching back to September.
A 1-1 draw for nearest challengers Brest against Lille earlier on Sunday means the Parisians are now 12 points ahead at the Ligue 1 summit with only eight games left, and a 10th title in 12 seasons is an inevitability.
Mbappe completed the whole 90 minutes of a Ligue 1 game for the first time since informing the club in mid-February that he intended to leave at the end of the season when his contract expires.
His hat-trick, his third of the campaign, took him to 24 goals in Ligue 1 this season, and 38 in all competitions.
Portugal midfielder Vitinha opened the scoring in the 14th minute, collecting Mbappe’s pass 25 metres from goal before curling a low shot into the bottom-right corner.
Mbappe then made it 2-0 on the counterattack, feeding Randal Kolo Muani and then sprinting to get the ball back and slot into the far corner from a tight angle.
Montpellier got one back when Danilo Pereira could only help on a cross from the left and Nordin — a friend of Mbappe’s as a youngster at Clairefontaine, France’s national youth academy — headed in at the back post.
The home side then won a penalty right on half-time when Tanguy Coulibaly pounced on Pereira’s short back-pass before being clattered by PSG goalkeeper Gianluigi Donnarumma.
Teji Savanier smashed in the spot-kick, but PSG were back ahead five minutes after the restart as Mbappe scored with a superb shot from range, in off the underside of the crossbar.
South Korean star Lee made it 4-2 on 53 minutes, playing a one-two with Kolo Muani and firing in from outside the area on his left foot.
Mbappe then completed his hat-trick with a right-foot finish after latching onto a ball over the top, before Montpellier had a second penalty award overturned following a VAR review.
Warren Zaire-Emery hit the post for the visitors, and Mendes made it 6-2 a minute from time, bursting into the box to run onto a Vitinha pass and fire in.
AFP