James Vandenberg added 228 yards passing for the Hawkeyes (2-1), who beat the Panthers, a Football Championship Subdivision program, for the 15th straight time despite losing backs Damon Bullock and Greg Garmon to injuries.
Weisman, a sophomore with 8 career yards rushing coming into the game, scored from 1, 1 and 2 yards out to help Iowa avoid its third straight home loss dating to 2011.
The Hawkeyes nearly lost to Northern Iowa in 2009 before rallying for a 17-16 victory in a season that later saw them win the Orange Bowl.
This one wasn't quite that close - but Iowa still wasn't comfortable until late in the fourth quarter.
Iowa opened up a 24-13 lead just four plays into the third quarter, as Kevonte Martin-Manley's 51-yard reception set up Weisman's final TD of the day. But the Hawkeyes followed with a pair of three-and-outs, and they needed a key stop to hold Northern Iowa to Tyler Sievertsen's 25-yard field goal, which made it 24-16 late in the third quarter.
Iowa got to the Panthers 1 early in the fourth, and the Hawkeyes settled for a 19-yard field goal from Mike Meyer.
Northern Iowa stuffed Weisman on a similar situation with 2:54 left, but the Panthers didn't have nearly enough time to mount a serious comeback.
David Johnson had 77 yards rushing, 77 more receiving and a touchdown for Northern Iowa.
Iowa's defense held its opponent without a touchdown in the second half for the second straight week. But the Hawkeyes had issues with the Panthers attack in the first half.
Northern Iowa blew past Iowa's stunned defense to open the scoring, as Johnson's 1-yard score capped an 83-yard drive to put them ahead 7-0 just 4:24 into the game.
It was the second week in row that Iowa allowed a touchdown on its opponent's opening drive. But after being held without a touchdown in last week's 9-6 loss to Iowa State, the Hawkeyes broke through on their first two possessions.
Iowa ran the ball on nine of its first 10 plays - with eight carries by Bullock - and Weisman's 1-yard TD run made it 7-7. The Panthers answered with Sievertsen's 49-yard field goal, but Weisman capped another long drive with his second 1-yard touchdown of the day to make it 14-10 Iowa with 11:09 left in the first half.
The Hawkeyes and Panthers traded field goals and Iowa went into the break with a 17-13 lead.
Bullock, who rushed for 150 yards and the game-winning touchdown in an 18-17 win over Northern Illinois on Sept. 1, had 77 yards on 13 carries before he got knocked in the head early in the second quarter.
Garmon, Bullock's freshman backup, was knocked out later in the half with what appeared to be a right arm injury. That left the Hawkeyes without a true running back for the rest of the game.
The situation forced Iowa to turn to Weisman, who proved more than up to the challenge.