Kostyuk trailed Pegula 5-1 in the first set before winning five straight games, including twice breaking the top seed on serve. Pegula regrouped to tie the match at 6-6.
Kostyuk, who came from behind to defeat fourth-seeded Anastasia Pavlyuchenkova of Russia in a quarter-final match on Friday, then broke away from a 3-3 tie in the tiebreaker. She won the set on her second set point.
Boulter won 88 per cent of her first-serve points, to 62 per cent for Navarro. She also dominated by winning 67 per cent of return points on second serve.
Austin Open
Sixth-seeded Xiyu Wang of China clinched a two-set victory in a tiebreaker to top seed Anhelina Kalinina of Ukraine, 6-3, 7-6 in Austin, Texas. Wang's opponent in Sunday's final will be compatriot Yue Yuan, the eighth seed. She dispatched Anna Karolina Schmiedlova 6-0, 6-3.
Wang broke away from a 3-3 tie to win the first set over Kalinina, but they battled throughout the second set, with each player losing her serve twice en route to the 6-6 tie.
Kalinina led the tiebreaker 3-2, but Wang won three straight points, including on Kalinina's serve for a 5-3 edge. Kalinina won the next point, but Wang won the next two points on serve to take the match.