Bartoli beat giant-killer Lucie Safarova of the Czech Republic 7-5, 4-6, 6-1.
Also entering the last-four was top seed Victoria Azarenka of Belarus, who beat Belgium’s Yanina Wickmayer 6-0, 6-4 in another quarterfinal match which last just 57 minutes.
In the semifinal, Azarenka will take on Poland’s Agnieszka Radwanska who beat the USA’s Christina McHale 6-1, 6-1 in the last match of the day.
Earlier Stosur, the reigning US Open champion fired seven aces in the match which which lasted a little under two hours.
“I think it’s one of those matches where, when you’re in control, you’ve to keep going. I’m going to miss a few, but believe you’re going to hit more than what you’re going to miss. At the end of the day, I’m happy with the way I could bounce back in the middle of that third set,” said Stosur.
The semifinal line-up features four of the top five seeds with second seed Caroline Wozniacki being the only player to miss out.
Agnieszka Radwanska (POLx4) bt Christina McHale (USA) 6-1, 6-1
Marion Bartoli (FRAx5) bt Lucie Safarova (CZE) 7-5, 4-6, 6-1
Victoria Azarenka (BLRx1) bt Yanina Wickmayer (BEL) 6-o, 6-4
Samantha Stosur (AUSx3) bt Monica Niculescu 6-2, 2-6, 6-3
Samantha Stosur (AUSx3) vs Marion Bartoli (FRAx5)
Victoria Azarenka (BLRx1) vs Agnieszka Radwanska (POLx4)