World No.11 Badosa clinched a 7-6 (7-5) 7-5 victory on Thursday after spending two hours and 34 minutes on court.
Haddad Maia, coming off back-to-back wins at the United Cup, is at a career-high No.15 in the world after climbing from 82 at the end of 2021.
“I know she’s a fighter and it was going to be a very long match. She doesn’t give up. I really respect those kind of players,” Badosa said.
“It was a very physical match. It was very tough.”
Kudermetova came from a set down in the 4-6 7-6 (7-5) 6-1 victory and will face world No.13 Belinda Bencic for a place in Saturday’s final.
Swiss Olympic champion Bencic earned a late-night 6-2 3-6 6-4 victory over another in-form potential Australian Open contender, France’s world No.4 Caroline Garcia, in a high-quality duel that lasted one hour 53 minutes.