The 31-year-old Dutchman, a former world champion, won a sprint amongst his three breakaway companions, with Tobias Johannessen taking second and Tom Pidcock third.
"It was a super hard day. The start of the Tour was not great for our team, but I think, like always, we stayed calm," he said.
"We have a really nice group here, and we kept believing that it will turn around... but it's really nice to go to the first rest day with a win."
Having worked as a sprint lead-out man for his Alpecin Premier Tech teammate Jasper Philipsen - who had finished fourth and fifth in the sprint stages - in the previous two days, Van der Poel finally had a chance to go for a stage win for himself.
It was not until about halfway through the stage that an eight-man breakaway finally went clear on the steep 3.8km-long Suc au May climb.
Van der Poel then attacked out of that group with 25km left on the final categorised climb of the day, the 900m-long and equally steep Mont Bessou.
Only Norwegian Johannessen, Frenchman Alex Baudin and Briton Pidcock were able to follow, and then it was a full-throttle charge to the finish line with a 50-second lead over the significantly-reduced peloton.
'Roads were horrible'
The breakaway riders had plenty in the bag and even slowed down in the final kilometre in a cat-and-mouse game before the final sprint. But when Van der Poel launched that, it was clear that he would be too strong for the others.
"I was not so sure. I spent a lot of energy trying to keep the break alive," he admitted.
"There was a lot of pressure from the bunch. The roads were horrible for a breakaway with a headwind the whole day.
"We fought for it, and I'm happy to finish it off."