Pryor posted the first receiving and rushing scores of his college career for Wisconsin (10-0, 7-0 Big Ten), which entered Saturday as one of only five unbeaten teams in the nation.
Badgers outside linebacker Leon Jacobs had a fumble recovery for a touchdown, and another recovery that led to a score.
The Badgers endured despite a sloppy first-half effort on offense with two interceptions by quarterback Alex Hornibrook and a fumble from freshman running back Jonathan Taylor.
Wisconsin's defense held the Hawkeyes (6-4, 3-4) to 55 total yards. Iowa was 0-for-12 on third downs.
Iowa quarterback Nate Stanley, fresh off a five-touchdown performance in an overtime win last week against Ohio State, completed 8-of-24 passes for 41 yards and one interception.
It didn't take long for Iowa to get on the scoreboard. Hawkeyes cornerback Josh Jackson picked off Hornibrook less than two minutes into the game, returning the pick 43 yards for a score at 13:30 of the first quarter.
Pryor's first touchdown -- a 25-yard rushing score -- capped a five-play drive that lasted 5:51, and gave Wisconsin a 10-7 lead at 8:55 of the second quarter.
Pryor caught a 12-yard Hornibrook pass for a score with 1:19 left in the first half that pushed Wisconsin's lead to 17-7.
Meanwhile, Jackson maintained his solid effort and nabbed his second interception off a tipped pass in the third quarter, running it back 52 yards for an Iowa touchdown that cut Wisconsin's lead to 17-14 at 11:18.
Wisconsin extended its lead to 24-14 on a 21-yard score off a fumble recovery by Jacobs, when the ball squirted out amid a pile of players on the Iowa 21-yard line with 6:10 to go in the third quarter.
Wisconsin's defense continued its domination as inside linebacker T.J. Edwards leapt to intercept a Stanley pass on a one-handed grab at the Badgers' 41-yard line with 18 seconds left in the third quarter.
Hornibrook completed 11 of 18 passes for 135 yards, with two touchdowns and three interceptions.
NOTES: Wisconsin QB Alex Hornibrook has thrown an interception in seven straight Big Ten Conference games. ... Badgers coach Paul Chryst said two days ago that Quintez Cephus, team's leading receiver, was ruled out for the remainder of the season due to a right leg injury. ... Iowa junior CB Joshua Jackson has had five interceptions in the last two games.