Stosur had the misfortune of running into World No.1 Serena Williams in the second round of her last two events in Montréal and Cincinnati, and World No.8 Bouchard is hardly an easy draw either, though Stosur had won their most recent meeting in last year's Osaka final.
Stosur was in complete control of Wednesday's clash, breaking serve four times, saving all four break points on her own serve and dropping just seven points on her first serve en route to a 6-2, 6-2 win.
"I played really well from the first point to the last and really made life difficult for her," Stosur said. "I'm really pleased with my performance."
Bouchard said former US Open champion Stosur was just too good on this day.
"Sam was serving amazing and hitting amazing shots," Bouchard said. "You have to give her credit.
"You can't play amazing every week. It's been a little bit of a journey since Wimbledon, but I've been improving the whole way and hopefully I can get a few days practice and be ready for the US Open."
In her first WTA quarterfinal since her first event of the season in Hobart, Stosur will take on Kirsten Flipkens. The Belgian rallied from a 6-4, 5-3 deficit in outlasting Andrea Petkovic in three hours and 11 minutes, 4-6, 7-6(4), 7-6(6). In the process, she ended a three-match skid against Petkovic.
"We both played a very high level of tennis," Flipkens said. "Andrea is a great player and it's always a great challenge to play against a Top 20 player. Even though I was down 6-4, 5-3, I had the feeling that if I could hang in there, the match could change. And that's what happened.
"It's sad in tennis sometimes that there has to be a winner and a loser. We both deserved to win. It was one of the best battles I've had in my career."
Muguruza won six of seven games from 2-0 down in the third set for a 6-2, 3-6, 6-3 defeat of qualifier Peng Shuai.
"I'm playing well," Muguruza said. "This tournament is giving me confidence that I'm in good shape for the US Open."