Adam Robinson added 95 yards rushing for the Hawkeyes (4-1, 1-0 Big Ten), who recorded their biggest win ever over Penn State.
Iowa raced out to a 17-0 lead late in the first half on Stanzi's 9-yard TD pass to Derrell Johnson-Koulianos and his 1-yard plunge.
The Hawkeyes stopped Rob Bolden on fourth-and-goal from the 1 in the third quarter, and Shaun Prater returned an interception 33 yards for a TD with 1:27 left.
Bolden had 212 yards passing for Penn State (3-2, 0-1), which has scored just six points in a pair of road losses to Alabama and the Hawkeyes.
Iowa's 21-point victory surpassed its 19-0 win over the Nittany Lions in 1930.