The Lotto Soudal long range specialist left his breakaway companion Axel Domont (AG2R) with under 8km to go and held on to the finish even as his lead withered away.
Diego Ulissi (UAE Team Emirates) rounded out the podium positions while Richie Porte (BMC), Chris Froome (Sky), Alberto Contador (Trek-Segefredo) and the rest of the key contenders all finished safely in the bunch.
"I had good feelings all day long," De Gendt said. "The start was really hard. But I thought it was worth going flat out on the first hill. The course suited me very well today.
"At some stage, we had six minutes lead. I knew in the downhills we'd go at last as fast as the peloton. I was going for the polka dot jersey but I can't wear it tomorrow because I have the yellow as well."
Joining De Gendt and Dumont in the original break was Antonio Nibali (Bahrain-Merida), Romain Sicard (Direct Energie), Silvio Herklotz (Bora-Hansgrohe) plus Delko Marseille Provence KTM pair Delio Fernandez and Angel Madrazo, but all fell by the wayside as the pace and pressure increased.
De Gendt won by 44 seconds and with an added bonus, he has a handy overall lead as he heads into the 171k second stage from Saint-Chamond to Arlancand and the rest of the race. He also leads the mountains and points classifications.
"I hope I can keep it [yellow] until the time trial, it's a really good publicity for the team. After the Mont du Chat, we'll lose it," he said.
"I hadn't won a stage of the Dauphiné yet but I wanted to do it as well. I've tried many times in previous editions. It's a very nice race with very nice climbs. I'm delighted to lead it."
