The two teams traded scores through the first half, with the Wildcats taking a 20-17 lead into the break on Pitts' interception return with 12 seconds left in the second quarter.
Schaefer hooked up with Lee for a 9-yard touchdown early in the third quarter to give Towson a 24-20 lead.
Ball's second touchdown of the game later in the third gave Villanova a 27-24 advantage. Louis Adeyemi pushed the lead to 34-24 early in the fourth with a 1-yard TD run.
Schaefer made it 34-31 with a 2-yard TD pass to John Godlasky with 5:12 left, but the Wildcats controlled the ball for the rest of the game -- aided by an 11-yard pass from Whitney to Phil Atkinson on fourth-and-5 in the final minute -- to hang on for the win.
Ball rushed for 62 yards on 23 carries and Matthew Szczur had 68 yards on eight carries for Villanova.