The Dutchwoman clocked a time of seven minutes and 25 seconds, which was five seconds quicker than American Chloe Dygert. Vollering's compatriot, Loes Adegeest, came third.
Dutchwoman Charlotte Kool of Team DSM–Firmenich lost the yellow jersey, having earlier won her second consecutive Tour de France Femmes stage.
"I really didn't see this coming. I had no idea that I could do this today. I'm really surprised. I had no expectations. I really wasn't even thinking of the podium. The first days were just days that I needed to survive," Vollering said.
"Today, I was already thinking of stage four, a stage I really love.
"I did two power naps today after stage two. Before the start, I just flew into it. I stayed so calm. It was a strange day for me. It's nice that I have the yellow jersey. It's up to the other teams to take it."
The fourth stage is a 122.7-km ride from Valkenburg to Liege.