Wisconsin (11-2) is now headed to its second straight Rose Bowl.
Ball ran 27 times for 137 yards and caught a TD pass, giving him 38 touchdowns this season. That's one short of Barry Sanders' single-season record.
Russell Wilson was 17 of 24 for 187 yards with three TDs and no interceptions. He set a new NCAA record with a TD pass in his 37th straight game. Texas Tech's Graham Harrell had the previous mark of 36.
The Big Ten's first championship game made the idea of a conference title tilt seem like a good one.
Michigan State (10-3) rallied from a 21-7 first-quarter deficit to take a 29-21 halftime lead and still led 39-34 after Dan Conway's 25-yard field midway through the fourth quarter.
But Wilson and Ball answered with a score and a 2-point conversion.