Iowa (4-3, 1-2 Big Ten) ended its three-game losing streak.
Indiana (2-4, 0-3) had two turnovers, costly penalties and a missed extra point and failed to manage so much as a first down on six of its first eight possessions. The Hoosiers lost their fourth straight, three of those at home, and their hopes of reaching bowl games in back-to-back seasons for the first time since 1990-91 took a significant shot.
It was downright ugly in Bloomington, where fans booed throughout the game and many students left before the end of the third quarter.
The Hoosiers wanted to follow the script provided by Pittsburgh, Northwestern and Michigan State the previous three weeks -- stay close to Iowa and win it late.
But Stanzi refused to go along.
The sophomore quarterback found the perfect remedy for his recent struggles in Indiana's defense. Stanzi finished 12-of-20 for 184 yards. He also got help from Shonn Greene, who ran 23 times for 115 yards, and Hampton, who ran 22 times for 114 yards. It was Greene's seventh straight 100-yard game this season.
Against that combination, mistake-prone Indiana couldn't stay close.
Iowa's Brett Greenwood picked off Kellen Lewis' third pass of the game, returning it to the Indiana 11. Four plays later, Trent Mossbrucker made a 26-yard field goal.
After Indiana endured its second straight three-and-out, the Hawkeyes took advantage again. This time, Hampton scored on a 1-yard plunge to make it 10-0.
It was just the start.
Greene sliced through the Hoosiers defense on a nifty 12-yard scoring run to make it 17-3 early in the second quarter, and Stanzi opened the second half with a 34-yard TD pass to Andy Brodell and a 20-yard TD pass to Brandon Myers to make it 31-9.
Hampton scored again in the final minute to close out the scoring.
The Hoosiers' only spark came just before halftime when Lewis hooked up with Terrance Turner on a 17-yard TD pass. But Austin Starr pushed the extra point wide right, and Indiana, which had 286 yards in offense, never recovered.