Yastremska saved a championship point on her way to the title with the 19-year-old putting on a fearsome display of firepower in a match lasting a minute short of three hours.
"You've always been my idol, thank you for this match," Yastremska said.
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"I was here two years ago and I lost in the first round. I almost lost at match point today but I'm happy to win."
Garcia took an early lead in the opening set but Yastremska fought back to level at 3-3 with powerful baseline shots.
Caroline Garcia à Strasbourg
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The Ukrainian stepped up her game to take the set with a mixture of baseline rallies and occasionally coming to the net to outfox her opponent.
Yastremska's devastating forehand kept her in control in the second set and she held a 5-3 lead which gave her a chance to serve for the title.
Garcia saved two championship points, however, and forced a deciding set as Yastremska double-faulted.
After a tense final set Yastremska dominated the tiebreaker to join Kiki Bertens, Karolina Pliskova and Petra Kvitova as the only women to have won two titles this year.
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