The tournament's hird seed and wildcard, Stosur was taken the distance by Tomljanovic but triumphed 6-4 3-6 6-4.
The wihdrawal of key players has thrown the event wide open after Madison Keys and Jelena Jankovic, the top two seeds, both withdrew due to injury.
Top seed Keys was due to face France's Kristina Mladenovic in the quarter-finals of the clay-court event.
However, Mladenovic was handed a walkover after Keys withdrew with a right elbow injury, the American not wanting to exacerbate the problem with the French Open on the horizon.
"I was suffering this morning, I absolutely cannot play," Keys is quoted as saying by the tournament's official Twitter account.
"I have to be careful and get treatment in order to be ready for Roland Garros. It's very frustrating to give up a tournament, but I prefer not to take risks."
Second seed Jankovic did manage one set of her contest against Sloane Stephens. The Serbian lost the first set 6-1 before calling for the trainer due to an apparent groin injury, and was unable to continue.
Frenchwoman Virginie Razzano came from behind to beat Elena Vesnina 4-6 6-1 6-1.