World No. 1 Azarenka needed nearly 3 hours to defeat home-crowd favorite Mona Barthel 6-4, 6-7 (3-7), 7-5. Azarenka lost her serve five times, including twice in the third set. However, she recorded three of her seven breaks in the decisive set to advance.
Barthel had 13 aces but also 16 double faults.
Sharapova, the world No. 2, played 3 hours, 2 minutes in edging by fifth-seeded Samantha Stosur 6-7 (5-7), 7-6 (7-5), 7-5. The third set was even until the 11th game when Sharapova got her second break of the day. Sharapova won six more points (129-123) than Stosur in the match.
Saturday's semifinals will feature the Top 4-ranked women players as third-seeded Petra Kvitova and No. 4 Agnieszka Radwanska also posted quarterfinal wins.
Kvitova defeated Angelique Kerber 6-4, 6-4 on the strength of four service breaks. Radwanska was a 3-6, 6-2, 6-3 winner of No. 8-seeded Li Na by saving all five of the break points she faced in the third set.
Azarenka will go against Radwanska in one of Saturday's semifinals. Azarenka is 9-2 versus Radwanska, including 4-0 this year. Sharapova and Kvitova are 2-2 lifetime. Sharapova won a three-set match in the semifinals of the Australian Open earlier this year after losing to Kvitova in last year's Wimbledon final.
Notable deaths of 2014 [PHOTOS]