Beathard hit Damond Powell for a 62-yard gain to jumpstart the comeback and Weisman followed with a 10-yard sprint into the end zone for his first score. His second score gave the Hawkeyes their first lead.
James Conner rushed for 155 yards and a touchdown but was held in check during the second half as the Panthers (3-1) failed to improve to 4-0 for the first time since 2000. Chad Voytik passed for a career-high 250 yards but Pitt's last-gasp drive ended with an interception.
The Hawkeyes appeared lifeless at times in the first half as Pitt built a 17-7 lead behind Conner and sophomore wide receiver Tyler Boyd but coach Kirk Ferentz's decision to send in Beathard for Rudock provided a welcome spark.
The long-haired Beathard completed 7 of 8 passes for 98 yards, including a rainbow that Powell hauled in with one hand to set up Weisman's touchdown that made it 17-14 early in the third quarter. The teams traded field goals and the Hawkeyes took control for good with a plodding 13-play, 52-yard drive that included a pair of fourth-down conversions and ended with Weisman vaulting into the end zone.
Pitt had two opportunities to take the lead but Voytik couldn't hit Boyd - who finished with 10 receptions for 153 yards - on fourth-and-10 with less than 2 minutes to play. The Panthers drove into Iowa territory in the waning seconds but Voytik's pass over the middle to Boyd sailed high and into the arms of Iowa safety Anthony Gair.
The Hawkeyes raced onto the field in celebration after righting their season following a stunning loss to rival Iowa State a week ago. The Panthers trudged to the locker room in shock as their early momentum vanished.
Iowa came in seventh in the country against the run allowing all of 65 yards a game. Conner needed all of a quarter to top that total. Churning relentlessly behind a rapidly improving offensive line, the sophomore continued the best start by a running back in school history. He now has 699 yards on the season, well ahead of the pace set by Heisman Trophy winner Tony Dorsett in 1976.
Where Dorsett was a balletic mix of speed and grace, Conner is all blunt instrument. His 22-yard burst on Pitt's second possession set up a 13-yard dash by Chris James, the first rushing touchdown surrendered by the Hawkeyes this season.
Iowa responded with a bit of daring. Faced with fourth-and-2 at the Pitt 13, the typically buttoned down Ferentz opted to go for it, with Rudock finding a wide-open Henry Krieger Coble to tie the game.
No matter. Pitt went 75 yards in 18 plays, converting a pair of fourth downs in the process, with Conner's ninth touchdown of the year making it 14-7. The Panthers pushed it to 17-7 at the half when Voytik led a 66-yard drive that ended with a 33-yard Chris Blewitt field goal.