Sharapova, the tournament No. 1 seed, took out eighth-seeded Kirsten Flipkens 6-2, 6-2. She lost her serve once but ended up winning two-thirds of the points on serve and 60 percent of the points overall.
Errani was a 6-2, 6-3 winner over Elina Svitolina. She won more than half of the points off Svitolina's serve, which allowed her to claim five breaks in eight receiving games.
While the Sharapova and Errani wins took little more than hour each, the other two quarterfinals were lengthy.
Anastasia Pavlyuchenkova defeated fourth-seeded Angelique Kerber 5-7, 7-3, 7-6 (7-3) in 2 1/2 hours and Alize Cornet lost the first four games of her match before beating Andrea Petkovic 7-6 (8-6), 5-7, 7-3 in a 3-hour, 2-minute-long match.
Sharapova will take on Pavlyuchenkova in Saturday's first semifinal. She took a three-set decision from Pavlyuchenkova in 2010 in their only previous meeting. Errani is 3-1 versus Cornet with all three wins coming last year.