Iowa State looked nothing like the team that rolled over Texas Tech 41-7 a week before and struggled to finish drives against the Big 12's worst defense.
But freshman quarterback Jared Barnett finally got the Cyclones (5-4, 2-4 Big 12) close enough for Guyer to kick his game-winner, leading a march from his own 13 to the Kansas 24. With the wind at his back, Guyer's kick sailed through the uprights, his second field goal of the day.
Kansas (2-7, 0-5) showed some spark after managing only 46 yards in a 43-0 loss to Texas, but missed two field goals and lost a fumble deep in Iowa State territory in suffering its seventh straight loss. The Jayhawks haven't won a conference game since beating Colorado, which no longer is in the Big 12, on Nov. 6, 2010.
Barnett, now 2-0 as a starter, ran for 125 yards on 22 carries and threw for another 175 yards, completing 16 of 30 passes with one interception.
He started the winning drive with a 17-yard completion to Aaron Horne, then sprinted 11 yards for another first down. Barnett later hit Albert Gary for gains of 11 and 6 yards before the drive stalled and coach Paul Rhoads called on Guyer, whose 32-yarder had given Iowa State an early 3-0 lead.
Iowa State's Stephen Ruempolhamer sacked Jordan Webb three plays later to force a punt, and the Cyclones, taking over with 2:37 left, kept the ball the rest of the way as Woody ripped off runs of 6, 8, 6 and 25 yards.
The Cyclones finished with 426 yards of total offense against a team that had been allowing an average of 559 a game in league play. Iowa State now is within one win of bowl eligibility, but the Cyclones have a tough road the rest of the way, finishing against Oklahoma, Oklahoma State and Kansas State.
Both teams wasted good scoring opportunities, and that was especially costly for Kansas.
After taking a 7-3 lead when D.J. Beshears scored on a 22-yard reverse late in the first quarter, Kansas drove to the Iowa State 32, 19, 23 and 2 on consecutive possessions and came away with only three points.
Alex Mueller had a 49-yard field goal attempt blocked by A.J. Klein, then was wide right on a 36-yard attempt, and James Sims lost a fumble before Ron Doherty kicked a 19-yard field goal to tie the score at 10 in the third quarter. The Cyclones stiffened on that drive after Kansas had first-and-goal at the 4.
Iowa State had taken a 10-7 lead on wide receiver Aaron Horne's 18-yard touchdown run on a reverse. Horne came around from the right side, turned the corner, squirted through a group of tacklers at the 10 and raced to the end zone to finish an 11-play, 80-yard drive.
The Cyclones seemed on the verge of taking a 17-10 lead early in the fourth quarter when Barnett and Woody missed a connection on a handoff on second-and-1 at the KU 9. The ball came loose, and Patrick Dorsey recovered for the Jayhawks. Punter Kirby Van Der Kamp had kept that drive going with a 17-yard run on a fake.
After the fumble, Iowa State forced the Jayhawks to go three-and-out on their next two possessions - the first time that had happened all day - and Barnett directed the drive to Guyer's go-ahead field goal.
Kansas showed an effective running game after being held to minus-2 yards on the ground by Texas. The Jayhawks rushed for 174 yards, but had only 4 yards on the ground and 15 total yards in the fourth quarter.
Webb finished 13 for 21 for 127 yards and no interceptions.