Marcus Coker added 113 yards rushing and a pair of touchdowns for the Hawkeyes (3-1), who raced out to a 28-3 halftime lead on the strength of a revitalized passing attack in their final tuneup before the start of Big Ten play.
Vandenberg threw for 198 yards in the opening half. His 1-yard TD plunge opened the scoring, and Vandenberg found Marvin McNutt for TD pass of 13 and 17 yards to put the Hawkeyes up by 25 late in the second quarter.
Louisiana-Monroe started the second half playing like the team some thought could give the Hawkeyes serious trouble.
By then, it hardly mattered.
The Warhawks finally found the end zone with 9:35 left in the third quarter, capping an impressive drive on a 4-yard touchdown run by quarterback Kolton Browning. Iowa simply drove right back down the field, jumping back ahead 35-10 on Coker's 2-yard run.
ULM answered with a 1-yard TD run by Tavarese Maye. But a failed onside kick set the table for Vandenberg's 23-yard TD pass to Keenan Davis with 39 seconds left in the third quarter that gave the Hawkeyes a 42-17 lead.
Wells and Browning combined for 293 yards through the air, but neither threw a TD pass. ULM couldn't do much on the ground either, rushing for just 59 yards on 30 attempts.
Iowa used a hurry-up offense to erase a 17-point deficit in the fourth quarter and stun Pitt 31-27 last week in the largest comeback in school history.
The traditionally conservative Hawkeyes went right back to a no-huddle look on Saturday.
It paid off with by far their best start of the season.
Vandenberg capped a 74-yard opening drive with a 1-yard plunge to put Iowa up 7-0 less than four minutes in.
ULM answered with Justin Manton's 43-yard field goal. But the Hawkeyes drove right back down the field, pushing their lead to 14-3 with 1:39 left in the first on a textbook fade pass from Vandenberg to McNutt from 13 yards out.
Micah Hyde took a Warhawks punt back to the ULM 29-yard line, and six plays later Coker ran for a 4-yard TD that put the Hawkeyes up 21-3.
Vandenberg and McNutt hooked up for a touchdown the fourth time this season with 2:07 left in the first half.
The 6-foot-4 McNutt sealed himself between the cornerback and the sideline and plucked his 17-yard TD grab out of the air, giving Iowa a 28-3 lead.
McNutt caught seven passes for 100 yards, reaching the 100-yard mark for the second game in a row.
Iowa players wore a green decal on their helmets, and many Iowa fans wore green shirts in honor of former Hawkeyes safety Brett Greenwood, who remains hospitalized after collapsing following a workout earlier this month. Greenwood started at safety from 2007-10 and was cut late in training camp by the Pittsburgh Steelers.
Greenwood's parents released a statement this week, saying he continues to make improvements.
Iowa will get next week off before opening play at Penn State on Oct. 8. The Hawkeyes will be in good shape in Happy Valley if Vandenberg keeps throwing the ball like he has lately.
Vandenberg has tossed for 669 yards and six touchdowns in his last two games.