The Hawkeyes converted two of Nebraska's three turnovers into touchdowns and got a short field for a third TD after the failed fake punt. Seven of Iowa's 14 possessions started on the Cornhuskers' side of the 50.
Iowa (8-4, 5-3 Big Ten) doubled its win total from a year ago and won a fourth road game for the first time since 2009.
Mark Weisman ran 24 times for 72 yards and two touchdowns for the Hawkeyes, and Rudock was 9 of 15 for 126 yards and two TDs.
Ameer Abdullah carried 23 times for 85 yards, the first time in nine games that he failed to rush for 100 yards. Ron Kellogg III, making his first career start, was 19 of 37 for 199 yards and a touchdown. He was intercepted twice in the first quarter.
The focus at Nebraska now shifts to whether first-year athletic director Shawn Eichorst will retain Pelini, who was penalized for unsportsmanlike conduct for protesting a pass-interference call in the third quarter.
Rudock left late in the third quarter with an undisclosed injury. Backup C.J. Beathard went three-and-out on his first full series, but the Hawkeyes got the ball right back when Ameer Abdullah fumbled at the Iowa 39.
Jordan Canzeri went 37 yards on first down, and Weisman scored from the 2 to put the Hawkeyes up 31-17. Beathard ran 4 yards on a bootleg for the final margin.
The Huskers had come from behind in the fourth quarter in each of their three November wins, but it wasn't meant to be as Kellogg, who walked on in 2009, made his first career start on Senior Day.
Iowa threw punter Sam Foltz for an 8-yard loss when he tried to run on a fourth-and-3 from his 32 in the third quarter. Rudock connected with Martin-Manley for a 24-yard TD on the next play to make it a two-touchdown game.
The Huskers had pulled to 24-17 when Kellogg hit Quincy Enunwa for a 15-yard touchdown on a fourth-and-3. It was Enunwa's school record-tying 10th TD reception of the season.
But Abdullah fumbled for a second straight game, and Weisman's touchdown with 9:17 to play gave Iowa a 14-point lead that was too much for the Huskers to overcome. Iowa, 6-0 this season when it wins the turnover battle, won for the fourth time in five games and ended a five-game losing streak in the series with Nebraska.
Now Pelini awaits word on whether Eichorst will bring him back for a seventh year. Though Pelini is 57-24 at Nebraska, his performance has been heavily scrutinized in the wake of bad losses to UCLA and Minnesota.
The question is whether Eichorst believes Pelini is moving the program in the right direction. The Huskers haven't won a conference championship since 1999, and they were eliminated from the Big Ten Legends Division race two weeks ago.
In addition to a run of blowout losses dating to 2011, Pelini came under fire in September after an audio of his profane tirade against Nebraska fans went public.