Marseille's win put them level on 69 points with third-placed Olympique Lyonnais, who beat Dijon 5-2 on Friday and are ahead of Marseille on goal difference.
Thauvin stole in front of his marker at the front post to open the scoring for Marseille early in the first half by heading Bouna Sarr's cross home from a tight angle.
On the half-hour mark he scored from the spot after Dimitri Payet was fouled in the box.
Striker Mitroglou netted a third in the 35th minute, rising high to steer Jordan Amavi's cross in at the far post, and he scored his second three minutes later with a close-range volley to put his side 4-0 up at the break.
Lille playmaker Yassine Benzia reduced the deficit by drilling a low left-foot shot into the net in the 54th minute, but winger Lucas Ocampos made it 5-1 with a powerful strike 14 minutes later.
That result, coupled with Toulouse's 2-0 win at home over Angers, leaves struggling Lille second from bottom on 29 points, four points adrift of the safety zone.
Monaco were looking to put some daylight between themselves and the chasing pair of Marseille and Lyon, but any chance of that went out the window when Jemerson was given a straight red for stopping a shot with his hand.
Jimmy Briand slotted home the resulting spot kick low to the goalkeeper's left, and 12 minutes later midfielder Etienne Didot executed a perfect strike to send a dipping volley flying into the bottom corner from just outside the area to make it 2-0.
Marcus Thuram, son of former French World Cup-winning defender Lilian, made it three early in the second half, and though Monaco pulled a goal back through Almamy Toure's header from a free kick, they could not reduce the deficit further.
Elsewhere, Amiens coasted to a 3-1 win over Strasbourg, while Caen defender Damien Da Silva's own goal was cancelled out by a Jessy Deminguet strike as they drew 1-1 with Metz.
(Reporting by Philip O'Connor; Editing by Toby Davis)
