Despite an assured start which saw her secure the opening set, the Australian crumbled in the second and continued to wobble in the decider.
But Stosur recovered to force a tie-break before reeling off five of the last six points to snatch victory from Mladenovic.
"Midway through that second set it actually felt like things were coming out a little bit cleaner, a little more solid," Stosur said.
"I was really pleased to come back after being two match points down and I think the third set was probably the best tennis I've played all week."
The Australian had also required a final set tie-break in her first round clash with qualifier Madison Brengle.
Kirsten Flipkens survived a scare of her own as she narrowly beat Storm Sanders 4-6 7-6(3) 7-6(5) while third seed Elena Vesnina was forced to retire with a hip injury when trailing to Spanish qualifier Estrella Cabeza Candela 4-6 6-2 4-1.