The Belgian was part of a six-rider escape early on the 171km second stage from Fribourg to the Marecottes ski resort.
Only Nys and Andrea Vendrame were still clear when they were caught and passed by Australia's Luke Plapp in the last kilometre. But Nys sprinted past for his first World Tour victory. Italian Vendramme was second.
"I wanted this victory so badly, I've worked so hard for it, I'll remember it for the rest of my life", said Nys, a former junior world cyclo-cross champion. His father Sven Nys won two full world titles in the discipline.
The pack, containing the race heavyweights, finished 16 seconds back.
Nys, who rides for Lidl-Trek, displaced Frenchman Dorian Godon at the top of the overall classification.
The Belgian leads Vendrame of Decathlon-AG2R by four seconds with Plapp, of Jayco-AlUla, third at 22sec ahead of Friday's 15.5km time trial.
"I'm not strong enough right now in the time trial to keep the yellow jersey, but I'm going to enjoy wearing it tomorrow," said Nys.
