Since winning the title in Carlsbad in August, Stosur has struggled for form and is in danger of finishing the year outside the Top 20 for the first time in five years. But despite a slow start, she looked in control throughout against Bencic, eventually running out a 64 62 winner in little over an hour.
"I feel good," Stosur, the Osaka champion in 2009, said. "I'm excited to be in the quarterfinals again here and overall I'm very happy with the way I played today."
Bencic, competing in just her fourth WTA main draw, is a relative newcomer at this level, although she was not an unknown quantity to Stosur.
"She won junior French and Wimbledon, so to win two Grand Slams as a junior she's showing some very good potential," Stosur said of her 16-year-old opponent. "I think she has a good game and is a smart player - she hits the ball very well when she's in position and she anticipates very well.
"I was expecting a tough match. We practiced last week, which was maybe good for me as we'd never played before and it gave me a chance to see some little things that made the match a bit easier."
Twelve months ago, Bouchard lost to Kumkhum in the final round of qualifying but was never in danger of suffering a similar fate this time around, breaking serve six times en route to her 37th win of the season.
"I definitely think it was closer than the score. She's very tricky to play and I actually lost to her last year in qualies so I was looking for my revenge," Bouchard said. "It was tough because it was raining this morning and I was rushed and didn't get to hit as much as I would have liked. But that's just part of the job and was an extra challenge.
"I think I'm playing well but I still have a lot of things to improve and these are good tournaments to try and work on my game. I want to end the season on a good note and then start getting ready for next year."