Aaron White scored 11 of his 13 points in the first half for the Hawkeyes (12-2, 1-0), who led by as many as 20 points in the second half.
Terran Petteway had 20 points for Nebraska (8-5, 0-1), which shot a season-low 29.9 percent from the field as it lost its 14th straight game to a ranked opponent.
White's breakaway two-handed dunk put the Hawkeyes ahead 55-35 with 8:16 left—the biggest lead of the game.
Nebraska stormed back with a 20-5 run, capped off by Petteway's 3-pointer with 1:45 left to cut the deficit to 60-55.
Nebraska got the ball back after an Iowa free throw, but Deverell Biggs' pass deflected off the rim for a turnover.
The Hawkeyes—who missed 17 free throws in the game—hit 7 of 10 from the line in the final 2 minutes to secure the win.
Walter Pitchford scored 13 for the Cornhuskers and Biggs added 12.
Iowa won despite making only one 3-pointer and being outrebounded. Nebraska put up 19 more field goal attempts than the Hawkeyes.
The Hawkeyes led 30-23 after a shaky first half where they went nearly 5 1/2 minutes without a field goal.
White jolted Iowa and the fans inside Carver-Hawkeye Arena with another dunk—this time an impressive reverse slam in transition.
A couple of minutes later, White made two free throws to tie the game 22-22.
Then White hit a rare 3-pointer—only his third of the season—to put the Hawkeyes back in front. White score two more baskets down the stretch to help Iowa end the half on a 12-1 run.
Iowa's Jarrod Uthoff scored 11 points.