Gordon topped 1,000 yards for the season on a 13-yard touchdown run in the third quarter that put the Badgers (5-2, 3-1 Big Ten) up 42-17. He finished the chilly, 40-degree night with 1,012 yards for the season.
Before the drives, Illinois (3-3, 0-2) found ways to claw back from an early 21-0 deficit and trailed 28-17 at halftime.
On a day when Michigan and Indiana combined for 1,319 yards of offense and 110 points, the decisive Badger drives looked like old-time Big Ten football -- using tough backs, smart running and short passes to put a lesser opponent away and stay close to Ohio State in the Big Ten Leaders division.
White took a short toss from Stave for his touchdown, lunging hard through a tackle to tuck the ball over the goal line. The touchdown ended a nine-play, 75-yard drive that chewed up just over five minutes and put Illinois on its heels.
Gordon's score wrapped up a five-play, 56-yard drive as he took the handoff and charged into the line, saw nothing there and used his speed to bounce outside and easily cover the 13 yards that put the Badgers up by 25 at 42-17.
Illinois was all but done and on its way to its 16th straight Big Ten loss.
The Badgers played most of the game without linebacker Chris Borland, the team's leading tackler. He hurt his right leg covering a Badger punt in the first quarter and never returned, watching much of the second half in street clothes. Team officials didn't immediately have any information about his injury.
Borland's absence didn't improve Illinois' ability to run the ball. The Badgers entered the game as the 10th-best run defense in the country, giving up 90.1 yards a game. Illinois didn't quite get there, finishing with 72 on 29 carries. Josh Ferguson led Illinois with 25 on seven carries.
Borland's backup, Marcus Trotter, made the most of his shot with a team-high nine tackles.
Wisconsin breezed to its 21-0 first quarter lead and Illinois spent the rest of the night trying to catch up.
Early touchdowns from Gordon and White put the Badgers in command.
Gordon's first-quarter touchdown covered 26 yards and showed off his speed. He ran into a small gap on the left side of the Illini line and, with speed that seemed to surprise the Illinois defense, quickly cut past what briefly looked like a potential tackler and sped into the end zone. With 6:03 left in the first quarter, Wisconsin led 14-0.
Illinois tried a reverse to open its next possession, but Scheelhaase couldn't handle backup quarterback Aaron Bailey's pitch, bobbling it before it dropped to the ground. Wisconsin defensive end Ethan Hemer recovered the ball at the Illini 8.
Three plays later, Stave hit tight end Brian Wozniak a yard deep in the end zone for an easy toss and, with the extra point, a 21-0 lead.
With all that, Illinois somehow stuck with Wisconsin over the first 30 minutes.
Bailey's 1-yard toss to tight end Matt LaCosse with 45 seconds left in the first half brought the Illini to within 11 at 28-17. Scheelhaase keyed the drive with a 15-yard pass to Martize Barr and a 39-yarder to Ryan Lankford.