Scheelhaase pushed his way into the end zone from 1-yard out with 13 seconds to play to keep Illinois (5-0, 1-0 Big Ten) undefeated just over 1 minute after the Wildcats ( 0-1) had taken a 35-31 lead on a 6-yard TD run by Jacob Schmidt.
Scheelhaase and the Illini started the deciding drive on their own 31 and were at the threshold of the end zone six plays later with the help of a 28-yard pass to A.J. Jenkins and a 22-yard run by Scheelhaase.
Illinois trailed 14-10 at halftime but scored 21 points in the final quarter to complete the comeback.
Scheelhaase finished the day 21-of-32 for a career-high 391 yards and three touchdowns. Jenkins caught a dozen passes for 268 yards and three scores.
Dan Persa was impressive as well, throwing for 123 yards and four touchdowns.