Sharapova, the tournament's defending champion, defeated Ana Ivanovic 7-5, 4-6, 6-4, with the match turning on a seesaw third set in which there were seven breaks.
The Russian star won 80 percent of the points off Ivanovic's serve in the set but did only marginally better on serve herself. She lost all three break points she faced but cashed in four of her five when receiving serve.
Sharapova, who had a first-round bye, beat Lucie Safarova 6-4, 6-7 (3-7, 6-3 in the second round.
She is to play third-seeded Angelique Kerber in the semifinals Saturday. Kerber defeated Yaroslava Shvedova 6-3, 7-6 (7-3) with a pair of breaks in each set.
Saturday's other semifinal has No. 2-seeded Li Na facing qualifier Bethanie Mattek-Sands. Li took out fifth-seeded Petra Kvitova 6-3, 7-5 Friday and Mattek-Sands was a 6-4, 6-2 winner over Sabine Lisicki.