Vandenberg passed for 273 yards, and McNutt caught nine passes for 151 yards.
Marcus Coker rushed for 139 yards on 30 carries for the Hawkeyes (7-4, 4-3 Big Ten), who had lost their three road games by a combined 14 points.
The Hawkeyes outgained the Boilermakers 408 yards to 286 but struggled to put away scrappy Purdue.
The Boilermakers (5-6, 3-4) need to win Saturday at Indiana to become bowl-eligible.
Iowa scored on its first possession with a 26-yard touchdown pass from Vandenberg to McNutt.
Iowa answered when Vandenberg found C.J. Fiedorowicz for a 5-yard touchdown pass to make it 14-7.
Purdue's Carson Wiggs considered a fake punt but decided to kick while running instead. It was blocked by Collin Sleeper, and Iowa recovered at the Purdue 9. The Boilermakers caught a break when Mica'il McCall fumbled on the second play of Iowa's possession, and Purdue's Will Lucas recovered.
After an exchange of punts, Marve stepped in at quarterback for TerBush and led the Boilermakers down the field. But Tanner Miller intercepted Marve at the Iowa 1-yard line.
On the next play, Vandenberg dropped back into his end zone and was pressured by Dwayne Beckford. Vandenberg fumbled as he was going down, and Purdue's Brandon Taylor recovered in the end zone to tie the score at 14.
Iowa took a 21-14 halftime lead on a 2-yard touchdown run by Coker with 31 seconds left in the second quarter. The Hawkeyes outgained the Boilermakers 257 yards to 117 and held the ball for more than 19 minutes in the first half.
Iowa's Mike Meyer kicked a 38-yard field goal, and then Vandenberg connected with McNutt again for a 51-yard touchdown on the first play of the fourth quarter to give Iowa a 31-14 lead.
Ralph Bolden's 11-yard touchdown in the fourth quarter after TerBush returned to the game cut Iowa's lead to 31-21.
Marve re-entered the game on a fourth-and-18 situation and completed a 22-yard pass to Edison. He closed the drive with what looked like a touchdown run, but he fumbled into the pylon for a touchback, and Iowa took over.
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Linebacker Myles Jack, who suffered a season-ending knee injury, said Thursday he decided to leave UCLA and enter the 2016 NFL draft because he wants to be compensated for his skills.
The tougher tests await down the road for No. 3 Baylor Bears, but coach Art Briles has seen enough of his Bears to know this is his best team.
A decision has been made that Randy Edsall will not be the football coach at Maryland next season, and discussions are taking place about how and when to separate, a source said Thursday night.
Florida State running back Mario Pender has been released from the hospital but could be given a medical redshirt if he cannot return to the field this season.
Tennessee chancellor Jimmy G. Cheek has issued a statement amid rumors that alleges coach Butch Jones fought and punched senior offensive lineman Mack Crowder during a fall practice session.
With the addition of a few tweaks, UConn football coach Bob Diaco is still planning to bring a rivalry trophy with him to Florida on Saturday when the Huskies play UCF.