But Australia's top-ranked female Maya Joint has been tipped from the tournament, hammered by Russia's world No.8 Mirra Andreeva 6-2 6-0.
Joint, ranked 32 in the world, suffered serious service yips against the top seed, holding just one game on serve in Thursday night's lopsided quarter-final.
Her compatriot Birrell, given a wildcard into the WTA 500 event, overcame Romanian qualifier Jaqueline Cristian 5-7 6-1 7-5 in her quarter-final.
Birrell's triumph came as the Adelaide title defence of American star Madison Keys was ended by rising Canadian Victoria Mboko.
The 19-year-old Mboko downed the reigning Australian Open champion 6-4 4-6 6-2.
Mboko, after last year rising from being ranked below 300 to now being world No.17, will play Birrell in the 27-year-old Australian's first WTA semi-final.
Birrell prevailed against Cristian in a long and absorbing battle.
"Just the momentum shifts and how we both fought, I think we both completely emptied our tanks," Birrell, the world No.107, said.
"Honestly, it's probably easier to say after winning, but it's one of the reasons I just love tennis so much, because it tests you physically and mentally.
"It wasn't just about tennis out there today. It was about who could fight and who could keep believing in themselves.
"I'm really proud of myself that I just kept doing that until the last point."
Birrell said the physical nature of the clash took a toll, despite the mild temperatures of around 20 degrees.
"Just the length of some of the points that we had, had the lactic acid pumping," she said.
"I'm not sure what would have happened if I had to keep playing that last game; I really needed that last point because I could really feel my right quad starting to cramp.
"I told myself that I'm an Aussie - I can't cramp under 30 degrees."
Russian-born Diana Shnaider, who defeated American Emma Navarro 6-3 6-3, will meet the top-seeded Andreeva in the other semi-final.
17°C