Australian Stosur - who has won just two titles since her 2011 US Open success, one of which came in Osaka last year - won by retirement against compatriot Jarmila Gajdosova.
Stosur led 7-6 (7-4) 1-0 before Gajdosova withdrew with an apparent ankle injury.
The top seed hit eight aces and made two breaks on the hard court at the WTA International event before Gajdosova retired.
Stosur will now play Kazakhstan's Yulia Putintseva in the quarter-finals. Putintseva beat sixth seed Heather Watson in straight sets on Wednesday.
Fourth seed Coco Vandeweghe was surprised on Thursday, with Croatian Ana Konjuh claiming a 6-2 3-6 6-3 win against the American.
Konjuh won 78 per cent of points on first serve in her win, which took almost two hours to compile.
Kazakhstan's Zarina Diyas enjoyed a much more routine triumph, the fifth seed thrashing Lara Arruabarrena of Spain 6-0 6-1, while American Lauren Davis was also rarely troubled. Davis beat Japanese qualifier Shuko Aoyama 6-1 6-1.