Williams will meet Lucie Safarova for the championship after Safarova disposed of Polona Hercog 6-0, 6-0.
Williams had a decided advantage in the rest department in her match against Stosur.
Because of rain delays Thursday, Stosur had to win two matches Friday to get to the semifinals. The second of those victories came against Venus Williams.
Serena Williams, meanwhile, did not have to play an entire set in winning her Friday quarterfinal match against Sabine Lisicki. Lisicki retired while trailing 4-1 in the first set due to an ankle injury.
Stosur was trying to become the eighth player to defeat both Williams sisters in the same tournament.
Serena Williams will attempt to win her 40th career championship and has not lost to Safarova in four career meetings. Safarova has won five tournaments, but none in the last four years.
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