Vollering was one of several riders involved in a crash six kilometres from the finish and the Dutchwoman looked in pain as she battled to the line to limit the damage done in the general classification.
The peloton was chasing down a group of three riders when the incident happened on a sharp bend and Poland's Niewiadoma, who began the day third overall and 34 seconds off Vollering, made the most of the crash to take the yellow jersey.
In the end, it came down to a battle between Vas and Niewiadoma for the stage win and it was the Hungarian who claimed a narrow victory, with Germany's Liane Lippert coming in third.
"It's crazy, I still can't believe it. I don't know what to say; I did not expect this today because I felt so bad during the race," Vas said.
"My radio was not working so I did not know what happened at the back but Demi crashed so I think we lost the yellow so it's a shame and now I have mixed feelings."
Niewiadoma, of Canyon-SRAM Racing, had lost out on stage four in a sprint finish, coming in third behind the Dutch duo of Puck Pieterse and Vollering, but she now has the consolation of the overall lead, having finished third the previous two years.
"It feels very special for sure, I just learned about getting the yellow jersey a couple of minutes ago so I feel like it still didn't really reach me, but super happy," Niewiadoma said.
"Today's stage was very chaotic in general, I feel like all the stages so far were very hectic and dangerous, so we knew that we just had to stay in the front."
The Pole has a 19-second lead over American Kristen Faulkner, who finished fourth on the stage, a 152.5-kilometre flat ride from Bastogne to Amneville. Pieterse, who also crashed, dropped from second to third, 22 seconds behind the leader.
Vollering's misfortune drops her to ninth overall with a gap of one minute 19 seconds to make up over the final three stages if she is to retain her title.
Friday's stage six is a hilly, 159.2-km ride from Remiremont to Morteau.
