In the last WTA event before the US Open, the world No.80 triumphed 5-7 7-5 6-4 in two hours and 33 minutes, topping her sole previous success on the 125k circuit.
Three competitive sets eventually led to Linette taking the victory, while Italian Giorgi lost her second final in the space of 20 days, having suffered the same fate in Washington.
Four of the first five games in the opening set produced breaks and Giorgi ultimately prevailed by striking to love on Linette's serve at 5-5 before converting the first of three set points.
But the Pole has scrapped hard all week, winning seven matches to reach the final, and claimed the second set with some clutch play.
She saved four break points at a critical moment to move 5-4 ahead and, despite failing to take two set points in the next game, ultimately got the break she needed.
Giorgi, ranked No.58, appeared to have regained the ascendancy by breaking in the first game of the decider. However, Linette saved another four break points to stop herself from falling a double break behind.
That changed the momentum and she subsequently rallied from 4-2 down, winning four straight games and claiming the first of two championship points when Giorgi put a forehand into the net, Linette celebrating by embracing her team.
Linette heads to Flushing Meadows on a high and could face defending champion Naomi Osaka in the second round of the US Open.