The third seed, who lifted the Suzanne Lenglen Cup in 2016, wasted little time on Court Philippe Chatrier, allowing Stosur only 10 points in the opening set as she sprayed the court with winners.
Hitting the ball like her life depended on it, Muguruza opened up a 2-0 lead in the second set but Stosur, who reached the final at Roland Garros in 2010, briefly fought back.
The Australian levelled for 2-2 but that effort cost her dearly as Muguruza bagged the remaining four games to set up a meeting with Ukrainian Lesia Tsurenko, who downed two seeded players on her way to the last 16.
"I had a tough opponent today, she's a Grand Slam champion and a former finalist here. I knew that if I didn't play my best tennis it would be very hard," said Muguruza, who ended the match with an ace.
"This court, I've been watching it since I was six to seven years old. Every time I come here it's so special."
