Snead, who finished with 11 catches for 135 yards, caught the winner in the back corner of the end zone for the Cardinals (3-1).
Ball State's Eric Patterson picked off South Florida's B.J. Daniels at the 10-yard line as time expired to seal the win.
Wenning was 24 of 36 for 244 yards passing with two touchdowns. Jahwan Edwards ran 98 yards on 16 carries and a touchdown for the Cardinals, who won their second straight game after being down late. Ball State beat Indiana, 41-39, on a field goal as time expired last week.
South Florida (2-2) lost its second in a row despite Daniels' efforts. He threw three TD passes and led the Bulls in rushing with 75 yards.