The Dutchwoman, who won the road race and time trial titles at the world championships last weekend, was again in a league of her to break the previous record of five wins held by compatriot Marianne Vos.
Four days after winning the world road race title, the Boels Dolmans rider followed an attack from Vollering on the steep climb before overpowering Cecilie Uttrup-Ludwig in the sprint.
"I think it was the closest of every year. It means a lot," Van der Breggen said.
"This finale is incredibly hard, winning six times is crazy."
Van der Breggen won her first La Flèche Wallonne in 2015, and has claimed victory at the famous race every year since.
She praised her Boels Dolmans teammates for helping her to make history on the Mur de Huy, where she also took over the lead of the Women's WorldTour.
"The team helped me a lot this year," she said.
"I felt some pressure to finish it off.
"Chantal (van den Broek-Blaak) and Amy (Pieters) did well to get me to the front and then I just waited until the final 150 metres to make my move."