Williams, who will move up to No. 29 in Monday's updated rankings, last won a title at the 2012 Luxembourg tournament.
Cornet had an early 2-1 lead with a service break, but Williams broke even in the fourth game.
After breaking Cornet in the sixth game, Williams failed to take advantage of two set points on the Frenchwoman's serve in the eighth.
Williams closed out the first set on a third set point with a clean backhand winner.
In the second set, it was Williams all the way as Cornet was unable to even win a game.
The 26th-ranked Cornet was attempting to post back-to-back wins over the Williams sisters.
On Friday, Cornet scored her first career upset over a No. 1-ranked player by beating Serena Williams 6-4, 6-4 in the semifinals.