"You've always been my idol, thank you for this match," Yastremska said.
"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.
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.
(Reporting by Rohith Nair in Bengaluru, editing by Ed Osmond)
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