Mark Weisman had a pair of short TD runs for the Hawkeyes (5-1, 2-0 Big Ten), who scored all but seven of their points in the first half.
Iowa scored 28 points in the first quarter - surpassing its total in each of its first four games against Power 5 school - and led by as much as 21.
Indiana pulled within 28-21, but Weisman closed the first half on a 1-yard TD run to give Iowa a 38-21 lead.
Tevin Coleman had 219 yards rushing for Indiana (3-3, 0-2), including TD runs of 83, 69 and 45 yards.
Hoosiers quarterback Nate Sudfeld left with an apparent injury in the first half and never returned.
Iowa insisted for weeks that it would rotate Rudock and C.J. Beathard in an effort to jumpstart its offense.
Rudock forced the coaching staff's hand though, completing 9 of his first 11 passes and helping Iowa to its highest-scoring half in nine years.
Indiana's terrible defense helped, too.
Beathard played just one series in the first half and went 0 for 2 passing. He also led a scoring drive in the fourth quarter and finished 2 of 5 for 9 yards.
But even Rudock's performance was overshadowed by one of the wackier first halves in Iowa history.
Iowa had neither scored nor allowed more than 24 points in a matchup with a fellow Power 5 school all season.
But the Hawkeyes and Hoosiers combined for seven touchdowns - including three one-play drives - in less than 20 minutes.
Rudock then silenced critics who questioned his ability to throw the long ball, finding Damond Powell for a 72-yard TD and a 21-0 lead.
A short run by Coleman then gave way to three plays that gained a combined 205 yards.
Coleman slipped through a few blocks and bolted 83 yards for a touchdown, the longest of his career. Iowa answered with a 60-yard sweep from Jonathan Parker to make it 28-7. Sudfeld responded with a 62-yard pass to Shane Wynn, and Nick Stoner's 13-yard TD grab pulled Indiana within 28-14.
Sudfeld's subsequent departure didn't matter much at first.
Coleman ran for a 45-yard touchdown on freshman quarterback Chris Covington's first snap.
But Covington only made the switch from linebacker to quarterback in preseason camp, and the Hawkeyes soon realized that they didn't need to worry about him beating them with his arm.
Covington finished just 3 of 12 passing for 31 yards and two picks, including a Jordan Lomax interception with 1:16 left that sealed it for Iowa.
The Hoosiers hung around in the second half, but Jordan Lomax's interception with 1:16 left sealed it for Iowa.
The Hawkeyes are now tied with atop the Big Ten with Minnesota.
Follow Luke Meredith on Twitter: www.twitter.com/LukeMeredithAP