Rybakina, the highest seed remaining in the women's draw, won nearly 82% of her first-serve points but converted only two of her 11 break-point chances en route to securing victory in two hours and 33 minutes.
"It was such a tough battle," Rybakina, a Moscow-born Kazakh, said during her on-court interview after reaching her fourth final of the year.
"I didn't serve that well and also Vika, from the second set, she was hitting the serve very well. It was difficult but I knew was going to fight until the end and actually that's what I did."
In the opening set, Rybakina squandered her first five break-point chances before solving Azarenka's serve to grab a 4-3 lead and she leaned on her astonishing power before closing out the 51-minute set with a hold to love.
Azarenka refused to go quietly, however, conjuring up a flawless display in the second set in which she limited Rybakina to five points and broke her serve three times to force a decider.
Rybakina, after a change of outfits, opened the third set moving much better and broke at the fifth attempt in the fifth game to move 3-2 up when Azarenka splashed a backhand into the net.
Rybakina crumbled in her first chance to serve out the match, however, as Azarenka got a break to get to 5-5 after she chased down a drop shot before her opponent sent a backhand volley into the net.
Rybakina, serving to stay in the match, held to love to force a tiebreak and she won the first three points of it before closing out the win.
Rybakina, a title winner this year in Brisbane, Abu Dhabi and Doha, will next face either American Danielle Collins (30) or Russian 14th seed Ekaterina Alexandrova (29).
