Weisman had 180 yards rushing for the Hawkeyes (1-1), who prevailed despite a somewhat shaky performance against an FCS opponent.
Weisman scored on runs of 10 and 3 yards to help the Hawkeyes take a 21-0 lead late in the third quarter. Missouri State answered with touchdowns on back-to-back plays from scrimmage early in the fourth quarter, pulling within 21-14 with 14:15 to go.
Rudock's 2-yard TD run put Iowa back ahead 28-14, and Tanner Miller sealed it with an interception in the end zone with 6:50 left.
Kierra Harris threw for 127 yards and a TD for Missouri State (0-2).
Even though the Hawkeyes had some early issues on offense, they still looked set to cruise to their first win in 11 months at the outset of the fourth quarter.
Ten seconds and 14 points later, Iowa found itself in a game that was suddenly much closer than it should have been.
The Bears finally got on the board with 14:25 left, as Julian Burton beat freshman cornerback Desmond King on a 27-yard TD reception. Rudock opened Iowa's next drive with a pass that was picked off by linebacker Rique Bentley, who took it back 28 yards for a TD.
Iowa answered with a 65-yard touchdown drive that consumed more than four minutes, and Miller's pick preserved some much-needed breathing room for the Hawkeyes.
Iowa's defense looked strong, holding the Bears to just 197 yards. But Iowa still led just 7-0 at halftime over a Missouri Valley Football school with just five wins over the past two seasons.
Iowa was plagued by dropped passes, negative rushes and a 33-yard missed field goal from Mike Meyer, usually a reliable kicker. The Hawkeyes had just one drive of note in the first half, a 69-yarder that ended with a 6-yard TD run from Rudock.
The Hawkeyes then drove to the Missouri State 2-yard line to open the second half, only to watch Weisman get stuffed on 4th-down-and-1.
Weisman redeemed himself a few minutes later, scoring from 10 yards out to give Iowa a 14-0 lead. Rudock then threw a perfect ball to George Kittle for a 47-yard reception, helping set up Weisman's second TD of the day.
Rudock threw for 193 yards in his second career start.
Though the Hawkeyes responded quickly to Missouri State's brief threat, they still have a lot to work on ahead of next week's rivalry game at Iowa State.
But so do the Cyclones, who had the weekend off after losing to FCS school Northern Iowa in their opener.
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Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.
Mike Bercovici passed for 273 yards and two touchdowns and ran for another score, and Arizona State got its season back on track with a 38-23 victory over No. 7 UCLA on Saturday night.
Florida State running back Dalvin Cook exited in the first quarter of the Seminoles' 24-16 win over Wake Forest with a left hamstring injury. He is day-to-day.
As if things weren't going bad enough at Texas, the Longhorns appear to have players on Twitter during lopsided losses and jabs at their coach accidentally being sent from other nearby teams.
Tulane long-snapper Aaron Golub became the first legally blind person to play in a Division I football game Saturday, according to the school.