Stosur, the No. 4-seed, finished off round-robin play with a 6-1, 6-4 win over eighth-seeded Tsvetana Pironkova. She had a pair of first-set breaks and moved ahead with a break in the seventh game of the second set.
That combined with fifth-seeded Elena Vesnina's 6-4, 3-6, 7-6 (7-1) win over No. 2-seed Ana Ivanovic to leave Stosur, Vesnina and Ivanovic with 2-1 Group B records.
However, Stosur, with the best sets won-loss record at 5-2, takes the group title and Ivanovic, who had a 5-3 sets record, also advances. Vesnina was 4-4 in her sets.
Group A was much more clear cut. Top-seed Simona Halep completed a 3-0 run through round-robin play Thursday and Pavlyuchenkova, seeded-sixth stopped No. 7-seeded Alize Cornet 6-2, 6-2 to claim the other semifinal spot from the group.
Halep goes against Ivanovic in one semifinal Saturday. Ivanovic won her only previous match against Halep, who retired after the first set in a match earlier this year. Stosur is 2-1 versus Pavlyuchenkova, although they haven't played since 2011.
Celebrity Breakups and divorces of 2014 [PHOTOS]