Rudock threw for a career-high 322 yards and completed 9 of 11 passes on the Hawkeyes' two scoring drives in the final 6 minutes.
Iowa (2-0) forced a fumble on Ball State's final possession to end the game.
Ball State (1-1) turned two fumbles into 10 points, but the Cardinals couldn't get a stop late. The Hawkeyes racked up 455 yards and 27 first downs.
Iowa broke through with a 12-yard touchdown pass from Rudock to Derek Willies with 3 minutes left to cap a 90-yard drive and cut Ball State's lead to 13-10.
After the Hawkeyes forced a punt, Rudock got the ball back with a chance to win.
Iowa likely didn't want to send out its shaky kicking game for a chance to tie after missing three field goals earlier in the game.
Rudock didn't force Iowa coach Kirk Ferentz to make that decision.
Rudock completed all four of his passes on Iowa's final drive, ending with a short check-down pass to a wide-open Duzey. The big tight end found a spot in Ball State's zone, turned around and ran straight into the end zone for the winning score.
Iowa fell behind 13-3 after missing three midrange field goals and losing two fumbles.
Ball State started the scoring with defensive tackle Blake Dueitt's 35-yard fumble return for a touchdown in the second quarter after Iowa mishandled the exchange on an end-around.
The Cardinals opened the third quarter with a long drive that led to a 42-yard field goal from Scott Secor. Iowa originally forced a three-and-out, but a running-into-the-kicker penalty extended the drive for Ball State.
Iowa's Jonathan Parker fumbled the ensuing kickoff return and Ball State recovered on the Hawkeyes' 23. But the Cardinals were forced to settle for a 27-yard field goal from Secor.
The kicking game was a question mark for the Hawkeyes during preseason camp and it nearly cost them Saturday.
Marshall Koehn missed field-goal attempts from 37 and 35 yards -- the second in the closing seconds of the first half.
Freshman Mick Ellis replaced Koehn for a 29-yard try in the third quarter. Ellis couldn't convert, either.
Iowa backup quarterback C.J. Beathard made his season debut on the second series of the game. He connected with Damond Powell on a sharp 38-yard pass in the end zone, but it was ruled an incompletion after replay.
Ball State struggled to move the ball against Iowa's defense.
Ball State lost its two previous games against Iowa by a combined score of 101-0.
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