The Hawkeyes (6-5, 4-4 Big Ten) reclaimed the "Floyd of Rosedale," a bronze pig given annually to the winner, with its sixth victory in seven tries over rival Minnesota (1-10, 0-7).
The Golden Gophers' beleaguered defense held Iowa scoreless in the second half, but Minnesota still lost its ninth straight under first-year coach Tim Brewster.
Minnesota went 96 yards in 15 plays and pulled within five on Adam Weber's 22-yard TD pass to Eric Decker with 1:38 left. But Weber's two-point conversion try fell incomplete, and Iowa recovered an onside kick.
Minnesota had burned its last timeout on an unsuccessful challenge in the second half, and the Hawkeyes ran out the clock to pick up their third straight win.
Weber was 24-of-41 for 190 yards and a touchdown for Minnesota, which has lost 10 games for just the second time in school history. Only a win against Wisconsin next week will prevent the program's first winless season in the Big Ten since 1988.
Trailing 21-10, the Gophers reached Iowa territory on three straight possessions between the end of the third quarter and the start of the fourth. Each time the Hawkeyes held them, including a fourth-down stop at the Iowa 37 with 8:22 left.
The Hawkeyes, who had rallied from early 14-point deficits for wins in each of the past two weeks, scored all their points in the first half.
Iowa went 80 yards in 10 plays to take a 21-7 lead with 50 seconds left in the second quarter. Young capped the drive with his second touchdown of the day, a 12-yard run.
Minnesota's Joel Monroe hit a career-long 54-yard field goal as time expired in the half.
Iowa went ahead 7-0 on an 8-yard touchdown pass from Christensen to Brandon Myers -- with an assist from James Cleveland, who let the ball slip through his hands. Myers was waiting behind the secondary, and the ball floated into his waiting arms.
The Hawkeyes made it 14-0 late in the first quarter on a 1-yard TD run by Young.
Minnesota, aided by a roughing the passer penalty, pulled within 14-7 on a 1-yard run by Justin Valentine with 4:33 left in the first half.
With a 22-yard run in the first quarter, Young became the third Iowa player to rush for 3,000 yards. Sedrick Shaw holds the school record with 4,156 yards.