Thauvin's effort was followed by Jordan Amavi's first goal since last December, a Pablo own goal and Josh Maja's late consolation.
The hosts move up to fifth in the table ahead of travelling to Olympiakos in Europe on Wednesday, their first appearance in the top-tier competition since 2014.
Central midfielder Michael Cuisance was handed his debut by coach Andre Villas-Boas after joining on-loan from Bayern Munich on transfer deadline day.
Playmaker Hatem Ben Arfa made his bow for the visitors as he returned to the club where he won the league title in 2010.
Thauvin opened the scoring after five minutes with a superb left-footed curling effort from outside of the box.
He was handed a chance to double the lead seven minutes later but opposition goalkeeper Benoit Costil saved the World Cup winner's penalty after Amavi was fouled.
Ben Arfa thought he had equalised at a near-empty Velodrome but the linesman lifted his flag for offside just after the quarter of an hour mark.
Amavi stretched the advantage nine minutes after the break as his looping header beat the backtracking Costil.
The former Aston Villa left-back then created the third with 25 minutes left as his shot was deflected past Costil by Pablo's attempted block.
Nigeria striker Maja cut the deficit with seven minutes remaining for his second goal of the season but Villas-Boas' men held on to move three points away from top of the table Paris Saint-Germain.
On Sunday, the highlight of the matches is the northern derby as third-placed Lille host promoted Lens in fourth.
On Friday, Kylian Mbappe scored twice in PSG's 4-0 win at Nimes.