Svitolina won in straight sets in tough conditions, though she needed two hours and two minutes to record a 7-5 6-4 triumph over her French opponent.
Cornet had won their previous meeting at Eastbourne in 2019 but the world No.68 was unable to pull off a repeat result against the tournament’s top seed in Illinois.
A see-saw contest saw 10 breaks of serve, starting with the second game as Svitolina struck an early blow while racing into a 3-0 lead.
However, Cornet clawed her way back to get on level terms and a tie-break looked likely until she was broken in a lengthy 12th game.
The second set followed a similar pattern as Svitolina again won the opening three games.
After a medical timeout, Cornet cut the deficit to 3-2 but was not able to get back on level terms, the pair exchanging six breaks through to the conclusion.
Having failed to serve out for the victory, Svitolina finally secured a first tournament triumph since Strasbourg in 2020 thanks to a superb backhand.
It is her 16th title overall and comes as ideal preparation ahead of the US Open, where the Ukrainian will face qualifier Rebecca Marino in the opening round in New York.