Stosur defeated 15th-seeded Dominika Cibulkova 6-4, 6-1 as she seeks a second Grand Slam title. Stosur won the 2011 U.S. Open and was a runner-up to Francesca Schiavone in the 2010 French Open.
Errani picked up her first semifinal slot in a major tournament with a 6-2, 7-6 (7-2) win over 10th-seeded Angelique Kerber. It was Errani's first win over a Top 10 player in 29 tries.
Errani opened with a solid first set, not facing a break point and getting a pair of breaks. The second set was a seesaw affair with eight breaks before Errani won the first three points of the tiebreaker -- two off Kerber's serve -- and then the last three to finish off the win.
Stosur and Cibulkova were fairly even in the first set but Stosur took control in the second, losing only five points on serve and cashing in three of her five break-point opportunities.
Stosur dropped serve just once and had only 13 unforced errors in her win. She claimed 52 percent of the points off Cibulkova's serve and finished with five breaks.
Stosur is 5-0 lifetime versus Errani, including a straight-set victory on a clay court earlier this year.
Wednesday's quarterfinals have second-seeded Maria Sharapova going against No. 23 Kaia Kanepi while fourth-seeded Petra Kvitova takes on qualifier Yaroslava Shvedova.