Birrell put on a clinical display to win the opening set at Pat Rafter Arena on Friday, but it was world No.55 Kalinina who prevailed 4-6 6-1 7-5 in two hours 41 minutes.
The Ukrainian has progressed to a semi-final match against either world No.64 Ashlyn Krueger or the 107th-ranked Polina Kudermetova, while Birrell will focus her attention on qualifying for the Australian Open.
Anhelina Kalinina hits a forehand during her win over Aussie Kimberly Birrell. (Darren England/AAP PHOTOS)
It was an anti-climactic ending to Birrell's summer run in Brisbane, having claimed the scalps of second seed Emma Navarro and No.35 Anastasia Potapova on her way to the last eight.
The 26-year-old will at least leave the tournament as Australia's top women's player, rising 14 places in the live WTA rankings to a career-best 99.
It is a remarkable comeback for Birrell, who had lost three years on tour with an elbow injury.
She secured the opening back-and-forth set by claiming the first break point, proving cleaner with seven unforced errors to 13 in the first 49 minutes.
Kalinina then broke away for a 5-0 lead in the second, before taking it 6-1 and sending it to a deciding set.
Can you believe it?! 😳— wta (@WTA) #BrisbaneTennis pic.twitter.com/epzgDKpeqPJanuary 3, 2025
Spurred on by the high-spirited home crowd the Gold Coast talent went up 5-4 when Kalinina sent the ball into the net, but she was unable to break and seal the victory.
Birrell was undone in her next service game, broken for 6-5 before Kalinina wrapped up the contest on her serve.
World No.1 Aryna Sabalenka will take to the court later on Friday against Czechia's Marie Bouzkova.
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