"I had opportunities in the second set. I just let them slip. It was nice to be able to take a couple of my opportunities in the third. Certainly would have been nicer to get it done in straights today," Barty said.
The Australian world number 17 is looking for her second trophy of the season following her success at the Nottingham Open in June.
She next plays Aryna Sabalenka, who defeated 2016 finalist Dominika Cibulkova 7-5 6-3.
The pair last met at the Australian Open with Barty edging the Belarusian in the first round.
"I've really been waiting for our next one. She's a great player," Sabalenka said.
"I would like to say that she's a tricky player because she's playing slice, lobs, with spin. It will be not easy."
Local hope Wang Qiang eased past qualifier Monica Puig 6-3 6-1 to reach the last four.
"I'm just trying to do my best and put up my best performance," Wang said.
Up next for Wang is Estonia's Anett Kontaveit, who produced a dominant display to beat qualifier Katerina Siniakova 6-4 6-4.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
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