
The win lifted Marseille two places up to fifth on 25 points from 14 games, one behind third-placed Lille and fourth-placed Montpellier.
Lille were beaten 2-0 at Nice while Montpellier were held to a 2-2 home draw by Rennes, allowing Olympique Lyonnais to stay second on 27 points – 15 behind champions and leaders Paris St Germain, who have won all their 14 games.
Thauvin carved out his memorable treble for Marseille after Bakaye Dibassy had given 16th-placed Amiens an early lead.
He put the visitors level in the 26th minute after good work by Morgan Sanson, fired them ahead in the 80th minute from a free kick and then sealed the win in stoppage time after team mate Dimitri Payet had missed a penalty.
Two goals by Montpellier’s Andy Delort cancelled out Hatem Ben Arfa’s fifth-minute opener for Rennes but the visitors salvaged a point thanks to a 71st-minute penalty from Benjamin Bourigeaud.
Mario Balotelli set up Wylan Cyprien to fire Nice ahead against Lille in the 25th minute and Allan Saint-Maximin wrapped up the contest with a clinical finish in the closing stages.