The British No.3 only made it into the main draw at Indian Wells as a lucky loser when Sloane Stephens withdrew with a foot injury.
Having seized her chance with victories over Varvara Lepchenko and 16th seed Beatriz Haddad Maia, Â Kartal clinched her meeting with Sabalenka courtesy of a 7-5 6-3 win over Kudermetova on Monday.
"With a game style like hers, she's going to hit winners left, right and centre the entire match," Kartal told wtatennis.com about her opponent's big groundstrokes.
"It was just something I had already accepted and for me the most important thing was to hold serve and keep the scoreboard pressure on her."
Sabalenka breezed into the fourth round with a routine 6-1 6-2 win over Italian Lucia Bronzetti.
The Belarusian top seed brought her best to the California desert after suffering early exits at the Qatar Open and in Dubai.
Elsewhere, third seed Coco Gauff beat Greek Maria Sakkari 7-6 (7-1) 6-2, while Australian Open champion Madison Keys needed three sets to see off Belgian veteran Elise Mertens 6-2 6-7 (8-10) 6-4.
Liudmila Samsonova won a three-setter against 12th seed and fellow Russian Daria Kasatkina, 2-6 6-3 6-3.
Gauff overcame late nerves, serving six double faults in the final game before closing it out on her sixth match point with a forehand winner.
"Except the last game I thought I played a great match. Just trying to look at the positives," said Gauff, who had revenge on her mind after losing to Sakkari in the semi-final last year.
"Obviously I was a bit disappointed with the last game, but that's just the perfectionist in me."
Gauff next plays Swiss Belinda Bencic, while fellow American Keys secured her 14th straight victory to set up a fourth-round meeting with 19th seed Donna Vekic, who upset American 10th seed Emma Navarro 7-6 (7-5) 6-1.
With Reuters.
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