Delaware, which needed the game to stay in realistic contention for a bid, dropped to 7-5, 4-4.
When Delaware's Andrew Pierce scored on a 10-yard run to extend the Blue Hens' lead to 34-12 with just 1 minute, 24 seconds left in the third quarter, the Wildcats looked finished. After Pierce's score, the conversion kick was blocked, and that turned out to be a huge play.
In the fourth quarter, Villanova quarterback John Robertson completed 11 of 13 passes for 146 yards and three touchdowns. He also ran 13 times for 95 yards in the final period.
"After three quarters it had been getting quiet on the sideline," Robertson said.
It got noisy after he hit Joe Price on scoring passes of 11 and 21 yards. Price had missed the previous five games with two fractures in his vertebrae.
"I felt great out there," Price said.
Robertson hit a wide- open Gary Underwood on a 25-yard scoring pass to get the Wildcats within 34-32 with 1:45 left.
On the two-point conversion attempt, Robertson threw an incomplete pass.
Villanova kicker Chris Gough then recovered his own onside kick, giving the Wildcats the ball on their own 46.
"The guys immediately next to me are supposed to blow up the guys that are head up on us and hopefully there is a gap in there and I can get to fall on it, and that is what happened," Gough said.
Robertson marched the Wildcats into field-goal range and Hamilton kicked the first game-winner of his career.
Villanova set a school record with 34 first downs. The Wildcats' 626 yards of total offense were second most in school history.