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Iowa, which fell out of the Top 25 after squeezing out a 17-16 victory over Northern Iowa a week ago, had a much easier time in what's annually the state's biggest athletic event.
Tyler Sash tied a school record by making three of Iowa's five interceptions, and the Hawkeyes (2-0) also recovered an Iowa State fumble. Stanzi and the offense converted four of those turnovers into touchdowns.
Though he wasn't especially sharp against the Cyclones (1-1), Stanzi still completed 18 of 34 passes for 197 yards with two interceptions. That was more than enough to give coach Kirk Ferentz just his second victory in six games at Jack Trice Stadium.
Iowa had not won at Iowa State since a 40-21 victory in 2003. It was the most lopsided game in the series since a 63-20 Iowa rout in 1997.
Iowa State quarterback Austen Arnaud suffered through a miserable day, finishing 10 of 22 for 79 yards and four interceptions. Freshman Jerome Tiller replaced him with 4:18 left in the third quarter and finished the game. He was intercepted once.
The Cyclones now have gone 14 straight quarters without scoring a touchdown against Iowa.
Brett Greenwood added two interceptions for the Hawkeyes, and Jeremiha Hunter recovered a fumble, his second big play in as many weeks. Hunter had the last of two field goal blocks in the final seconds that preserved the victory over Northern Iowa.
He fell on Alexander Robinson's fumble at the Iowa State 48 early in the third quarter, setting up Stanzi's 7-yard touchdown pass to Allen Reisner, who caught the ball in the right flat and loped untouched into the end zone for a 21-3 lead.
Greenwood picked off his second pass a little more than 3 minutes later and returned it 17 yards to his own 48. Stanzi's 39-yard pass to Trey Stross set up freshman Brandon Wegher's first collegiate touchdown, a 1-yard dive.
Wegher, who scored 54 touchdowns as a high school senior last fall, carried 15 times for 101 yards.
Stanzi's 6-yard TD pass to freshman Keenan Davis capped an 84-yard drive that followed Sash's final interception.
Iowa capitalized on an onside kick that backfired and an interception to take a 14-3 lead during a first half filled with mistakes by both sides.
Stanzi and Arnaud both overthrew receivers or tried to force the ball into coverage. David Sims picked off two of Stanzi's passes, while Arnaud was intercepted three times.
Sash's second interception, on a ball tipped by Greenwood, set the Hawkeyes up at the ISU 24 late in the first half. Three plays later, Derrell Johnson-Koulianos got a step on cornerback Kennard Banks and laid out in the end zone to catch Stanzi's nicely thrown ball for an 18-yard touchdown that made it 14-3.
Iowa State went up 3-0 on Grant Mahoney's 46-yard field goal late in the first quarter. The Cyclones then tried to catch the Hawkeyes off guard with an onside kick, but Iowa's Bruce Davis fell on the ball at the ISU 46.
A personal foul on Banks, who wrestled Stross to the turf when both were out of bounds, put the ball on the Iowa State 12 and two plays later, Stanzi flipped a 1-yard pass to Brett Morse for a touchdown.
