The world No. 8 dominated the first set before losing the second to an inspired Alexandrova, but found her rhythm in the decider where she lost only three points on her serve to close out the victory.
Earlier, Hobart International winner Rybakina advanced to her third final in four events this season with a gritty 3-6, 7-5, 6-1 victory over Greek sixth seed Maria Sakkari.
The 20-year-old Kazakh, who saved two match points to get past French qualifier Oceane Dodin in the quarterfinals, was staring at defeat as she trailed Sakkari 5-4 in the second set.
But the world No. 25 won nine of the last 10 games of the match to storm into the biggest final of her career as she chases a third title.
Rybakina faces a potentially tricky test against second seed Bertens, who easily beat her in their only previous meeting, in the semifinals of the Rosmalen grass event in June last year.