Stave threw for 254 yards for the Badgers (4-2, 1-1 Big Ten), who rushed for 173 yards -- 96 in the fourth quarter.
The offensive struggles of the Illini (2-4, 0-2) continued, with quarterback Nathan Scheelhaase the only positive. He finished with 178 yards passing and 84 rushing as Illinois gained 287 yards overall.
Scheelhaase ran for a 5-yard touchdown in the first quarter and threw for an 8-yard touchdown to Ryan Lankford to make it 24-14 late in the game.
But Jared Abberdaris fielded the ensuing onside kick, and Montee Ball scored his second touchdown of the game to snuff any hopes of an Illinois comeback.
Ball has 59 rushing TDs in his career, nine shy of the NCAA record. He finished with 19 carries for 116 yards.
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