Garcia needed to polish off her semi-final against American Jennifer Brady on Sunday morning 4-6, 6-3, 6-3 after a rain caused havoc with the schedule over the past week in the Midlands.
The heavy load appeared to take its toll as Croatian Vekic romped through the opening set of the final.
However, Garcia composed herself to break back twice in the second set before closing it out on a tie-break.
The deciding set also went to a tie-break without a single break of serve, where again Garcia prevailed 7-4 to take her seventh career singles title.
Nottingham WTA results on Sunday (x denotes seeding):
Caroline Garcia (FRA x1) bt Donna Vekic (CRO x2) 2-6, 7-6 (7/4), 7-6 (7/4)
Caroline Garcia (FRA x1) bt Jennifer Brady (USA) 4-6, 6-3, 6-3