It was the first career WTA title for the Frenchwoman, who bounced back after a 3-5 deficit in the first set.
"When I was behind, I told myself to take heart and take some chances," said Parmentier after her first career final. "When I won the first set, I told myself 'come on, you can do it,' and I'm very glad I was able to do it. It was a wonderful week for me (and) I don't even understand how I played so well."
Parmentier collected a winner's check of $21,165.
Azarenka, who won the mixed doubles title at the U.S. Open last month, also was attempting to capture her first tour final.
"This was her best tennis of the week," Azarenka said. "But I didn't take my chances. I lost focus."