The two-time tournament winner played aggressively to win the opening set in just 30 minutes. Stosur then broke Ivanovic's serve in the second set to go up 5-3. But Ivanovic got the early break at 2-0 in the third set and cruised from there. She will play Russia's Elena Vesnina on Friday, with both still trying to secure a spot in the semifinals.
Vesnina outlasted Bulgaria's Tsvetana Pironkova 6-2, 4-6, 6-0 for her first victory at the tournament.
In Thursday's last match, top-seeded Simona Halep of Romania swept past Ukraine's Elina Svitolina 6-1, 6-1, to finish the round-robin phase unbeaten. She had already qualified for Saturday's semifinals.