Austrian Thiem will face Germany's second-seeded Alexander Zverev or Greece's Stefanos Tsitsipas in Sunday's final. Australian Barty will meet two-time Grand Slam winner Naomi Osaka of Japan, who downed defending champion Caroline Wozniacki 6-4, 6-2.
Thiem dropped the first set to Russian Karen Khachanov, but came roaring back to win 2-6, 7-6 (5), 7-5.
"I was disappointed to lose that set, but still I had the feeling that I'm not playing that bad. I just got a little more aggressive," said Thiem, who ousted Andy Murray in Friday's quarterfinals.
"I'm really proud that I was fighting like crazy through the whole match because Karen was playing exceptionally well today."
Barty advanced with a three-set victory over Kiki Bertens. The French Open champion traded breaks of serve in the third set before scraping past her Dutch opponent 6-3, 3-6, 7-6 (7).
"The quality from both of us was exceptional at times," said Barty, who credited new members of her backroom team and a better physical and mental outlook for the improvements she has made over the past 18 months.
"I'm pretty happy with the way I was able to fight and dig in," she added.