Greene had touchdown runs of 52, 34, 34, and 12 yards for the Hawkeyes (5-3, 2-2 Big Ten), who have answered a three-game losing streak with a pair of blowout wins.
He became the first Iowa player to rush for four touchdowns since Tavian Banks did it against Iowa State in 1997. Heís the only player in the country with over 100 yards in his first eight games of the season.
Dustin Sherer, making his first career start in place of Allan Evridge, was 17-of-34 for 161 yards and two interceptions for Wisconsin (3-4, 0-4). The Badgers, who reached as high as No. 8 in the polls in late September, have been outscored 86-23 the past two weeks.
Sherer finally got Wisconsinís offense moving on itís first two drives of the second half. But Iowa held the Badgers to field goals instead of touchdowns, as Philip Welch hit from 40 and 35 yards out to pull Wisconsin within 14-9 midway through the third quarter.
The Badgers would soon regret not finding the end zone.
Just three plays later, Greene outran Wisconsinís defense for his longest touchdown of the year, a 52-yarder that put the Hawkeyes ahead 21-9.
Paki OíMeara then blocked a punt to give Iowa the ball on the Wisconsin 33. Ricky Stanzi threw behind tight end Alan Reisner in the flat, but Reisner made a one-handed grab and, thanks to a key block from Brandon Myers, ran 16 yards to make it 28-9 with 1:38 left in the third quarter.
Sherer was picked off by Pat Angerer early in the fourth quarter, and Greene put a capper on his best day yet with a 34-yard touchdown run to give the Hawkeyes a 35-9 lead with 9:18 left.
Stanzi had 114 yards passing and a touchdown for Iowa, which reclaimed the Heartland Trophy after two straight losses to Wisconsin.
John Clay led the Badgers with 89 yards rushing, and Zach Brown added a late 21-yard touchdown run.
P.J. Hill injured his left ankle in the second quarter and did not return. He finished with 34 yards on eight carries.
The Hawkeyes, behind a pair of Greene touchdowns, led 14-3 at halftime.
Iowa went up 7-0 on its first possession, as Greene capped a 70-yard drive with a 12-yard TD run. His next score, a 34-yard run that made it 14-0 midway through the second quarter, was a thing of beauty.
Greene burst into Wisconsinís secondary, juked cornerback Chris Maragos and, after shaking off safety Jay Valiaís attempt to drag him down from behind, dashed into the end zone. That run put Greene over 1,000 yards for the season.
Welch got the Badgers on the board with a 42-yard field goal with 59 seconds left in the first half.