Central Michigan (2-1) pulled within 31-29 on Ryan Radcliff's 13-yard TD throw to Titus Davis. The Chippewas failed on the two-point conversion, but they recovered an onside kick and moved to Iowa's 30-yard line in part because of a personal foul on the Hawkeyes (2-2).
Harman had the wind at his back on his wobbling winner, handing Iowa one of its most improbable defeats in 14 years under coach Kirk Ferentz.
Radcliff threw for 283 yards and two touchdowns for Central Michigan, while Mark Weisman ran for 217 yards and three touchdowns in a losing effort for Iowa.
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The Hawkeyes will regret this ending for the rest of the year -- and perhaps for years to come.
Iowa appeared set to sneak out of Kinnick Stadium with a narrow victory after Weisman's 12-yard TD run with 2:18 left put the Hawkeyes ahead 31-23.
But Iowa's defense -- which hadn't allowed a second-half touchdown in two weeks -- broke down at the worst possible time.
Central Michigan moved 64 yards in just 1:33, and Titus walked into the end zone after his defender fell down. But Iowa's secondary forced Radcliff into a high throw on the conversion try, and the Hawkeyes once again looked to be in the clear.
The fun was just beginning for the upstart Chippewas.
Central Michigan was called for a delay-of-game penalty on its first onside kick. But all that did was provide another shot for the Chippewas, who recovered on their own 42-yard line.
Iowa defensive lineman Joe Gaglione got into it with a Central Michigan player and was called for a back-breaking 15-yard personal foul penalty.
Radcliff's 9-yard run set up Harman's winning kick, his fourth and certainly most critical kick of the day.
Central Michigan led 23-14 at halftime. Iowa's defense stiffened, and a 5-yard TD run by Weisman and a crucial 46-yard field goal from Mike Meyer gave Iowa a 24-23 lead with 8:07 left.
The Chippewas were held scoreless for the first 29:15 of the second half. But all anyone will remember are those final 45 stunning seconds.