The 25-year-old then rediscovered her touch in the second set, before stepping up her game in the final set tiebreak to earn three championship points at 6-3.
Second seed Vekic fired a stunning forehand to trim the deficit to 6-4, but Garcia responded with an ace to clinch victory after two hours and 36 minutes.
The final brought to a conclusion the rain-hit pre-Wimbledon tournament in Nottingham, with some earlier matches having had to be played indoors.
Vekic, for example, overcame Kristina Mladenovic in a quarter-final clash which started on the grass outdoors before being moved to the indoor hardcourts, where most play occurred during the earlier rounds.
(Reporting by Hardik Vyas in Bengaluru, editing by Ian Chadband)
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