Stosur, who won the event in 2009, defeated Virginie Razzano 1-6, 6-2, 6-4. Razzano was in control through the first set, winning 14-of-19 points off Stosur's first serve and posting three breaks.
But Stosur didn't face a break point the rest of the way, winning 75 percent of the points on serve while getting three breaks over the second and third sets.
Stosur moves to the quarterfinals where she'll play Jamie Hampton, who was a 7-5, 7-5 winner over Tamarine Tanasugarn in her second-round match. Hampton had three breaks in each set, allowing her to overcome four dropped service games of her own.
Japan's Misaki Doi lost her serve just once in a 6-3, 6-2 decision over Olga Puchkova. Puchkova had eight aces but Doi still won more than half (31-of-59) of the points when Puchkova served.
Chang Kai-Chen also earned a quarterfinals slot, beating Casey Dellacqua 7-6 (7-4), 6-3. Chang had six breaks in 11 receiving games.
Swim Week Miami Beach 2014 [PHOTOS]