One of Pryor's scores came on a 60-yard TD run to open the scoring in the first quarter and the Seminoles (12-2) never trailed after that.
E.J. Manuel completed 27-of-39 passes for 295 yards and touchdown and also scored on the ground, carrying the ball six times for 26 yards in Florida State's victory.
With his fourth bowl win in four years, Manuel joined West Virginia's Pat White as the only signal-caller in Division I history to accomplish the feat.
Kenny Shaw made six catches for 61 yards and Rashad Greene hauled in a scoring pass for the Seminoles, who were appearing in their 31st consecutive bowl game.
Jordan Lynch was limited to 15-of-41 passing efficiency for 176 yards, a touchdown and an interception for the Huskies (12-2).
He also ran the ball 23 times for 44 yards in the loss.