Arnaud's pass to Darius Darks keyed a third-quarter touchdown drive that put the Cyclones (5-4, 3-2 Big 12) ahead. They added two more TDs in the period to put it away.
Given up for dead after allowing 120 points in consecutive losses to Utah and Oklahoma, Iowa State has won two straight and needs only one victory in its last three games to become bowl eligible for the second year in a row.
Kansas (2-6, 0-4), meanwhile, continues to struggle under first-year coach Turner Gill and lost its 11th straight Big 12 game.
The Jayhawks, down to third-stringer Quinn Mecham at quarterback because of injuries, showed some spark early and led 9-7 at halftime on Jacob Branstetter's field goals of 34, 42 and 38 yards.
The Cyclones, looking flat after their upset at Texas a week ago, managed only five first downs in the opening half and got its only touchdown of the half on Lenz's spectacular punt return, the first by an ISU player for a score since 2006.
Lenz wove his way across the field after catching the ball at his own 38, then finally found a wall of blockers and tightroped down the left sideline to the end zone.
The touchdown fired up the crowd, but did nothing for the Cyclones' listless offense. They failed to convert on two tries after facing third-and-2 at the Kansas 37 and the Jayhawks drove 42 yards to get Branstetter's third field goal as time expired in the half.
But it all turned in the second half.
The Arnaud-to-Darks hookup put the ball on the KU 25 and five plays later, Alexander Robinson burst in from the 2 for a 14-9 lead. Robinson topped 100 yards for the second straight week and went over 3,000 for his career, finishing with 117 in 17 carries.
A sack of Mecham forced a Kansas punt on the next series and the Cyclones drove 89 yards in 16 plays for another touchdown, a 3-yard plunge by Jeff Woody. Iowa State had more first downs on that drive (6) than it managed in the entire first half.
Freshman Shontrelle Johnson left three defenders on the ground grasping air during a 33-yard touchdown run that made it 28-9 late in the third quarter.
Mecham, who had thrown only one pass prior to Saturday, went 22 for 33 for 149 yards, one touchdown and one interception -- a leaping grab by Jake Knott that set up Johnson's TD. Kansas didn't get its lone touchdown until Mecham tossed a 5-yard pass to James Sims with 7 seconds left.
Arnaud finished 16 of 26 for 168 yards and no interceptions after going just 4 for 10 in the first half. Iowa State finished with 400 total yards -- 278 in the second half.
Robinson ran his career rushing total to 3,088 yards, which ranks fourth in school history.
Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.
Tim Beckman is threatening legal action after Illinois fired him as football coach Friday amid allegations of influencing medical decisions and pressuring players to play hurt.
LSU offensive coordinator Cam Cameron revealed in a post-practice news conference that he has been treated for prostate cancer but plans to coach this season.
The woman who accused former Baylor defensive end Sam Ukwuachu of raping her in 2013 has hired a Title IX law firm to represent her in potential civil litigation.
Arkansas tight end C.J. O'Grady has been arrested by Fayetteville police and charged with driving while intoxicated and being a minor in possession of alcohol.