After requiring a final set tie-break to defeat qualifier Madison Brengle in the first round, Stosur was once again forced to go the distance, winning five of the last six points of the match, to edge over the finishing line, 64 26 76(7).
Despite the contest's tense finale, Stosur made a confident start, overcoming an early break to take the first set. From here the Australian lost her way, dropping a one-sided second set and then surrendering an early lead in the decider.
However, she maintained her composure to force a tie-break before summoning one final push to overcome a 6-4 deficit and book a quarterfinal meeting with Bojana Jovanovski.
"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."
Stosur was not the only big name to snatch victory from the jaws of defeat in Tasmania.
Twenty-four hours after upsetting Peng Shuai, wildcard Storm Sanders very nearly blew No.2 seed Kirsten Flipkens' challenge off course, before eventually going down, 46 76(3) 76(5). Next up for Flipkens is another talented youngster, Garbiñe Muguruza, who progressed when Yanina Wickmayer retired with a viral illness.