Thauvin, a 2018 World Cup-winner omitted from France's squad for next month's finals, opened the scoring before his perfect corner was headed in by Odsonne Edouard for Lens' second goal on Friday.
Djibril Coulibaly pulled one back for Nice on the stroke of halftime.
Lens's second-half substitute Abdallah Sima sealed the victory with 12 minutes remaining, sparking wild celebrations among the 50,000 Lens fans who travelled to Paris hoping to see their club claim a first trophy since the 1999 League Cup.
The triumph capped a remarkable season for Lens, whose only top-flight title came in 1998 and who finished runners-up to Paris St Germain in Ligue 1 this season.
Nice, meanwhile, face Ligue 2 side St Etienne on May 26 and 29 in a two-legged playoff to preserve their top-flight status.
After a shaky start from both sides, Lens, who had Robin Risser to thank for two spectacular saves, took the lead in the 25th minute when Thauvin collected Matthieu Udol's cross in the area and found the net with a clinical left-footed effort.
The Northerners doubled their lead in the 42nd with Edouard beating Maxime Dupe with a header from Thauvin's corner.
Coulibaly, 17, reduced the arrears on the stroke of halftime, heading home a Jonathan Clauss corner.
Nice came close to levelling on the hour, but Antoine Mendy's header crashed onto the bar.
But Lens wrapped it up in the 78th minute as Sima, who had replaced Edouard 12 minutes earlier, outmuscled two Nice defenders to beat Dupe with a low shot for his fifth goal in six appearances in the competition.
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