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.
Yurachek details why he hired Pittman
Arkansas AD Hunter Yurachek joins The Paul Finebaum Show and talks about why he wanted Sam Pittman to be the head coach and the success the Razorbacks have had so far.
Oregon Ducks say COVID-19 test results were false positives
Oregon says the COVID-19 test results of five football players were determined to be false positives.
Marshall-Florida International football game postponed because of COVID-19
Florida International had to call off this Friday's game against No. 19 Marshall because of a lack of available scholarship players due to COVID-19.
Jeremiah Alexander, No. 8 prospect in 2022, decommits from Alabama
Jeremiah Alexander, a linebacker who is the No. 8 prospect for 2022, tweeted Tuesday that he is decommitting from Alabama.
North Texas-UTEP football game postponed amid rising COVID-19 cases in El Paso
The game between North Texas and UTEP scheduled for Saturday in El Paso has been postponed due to the spread of COVID-19 in the region.
Mississippi State RB Kylin Hill not expected to play again this season, sources say
Mississippi State running back and All-SEC selection Kylin Hill is not expected to play for the team again this season, sources told ESPN, having indicated to the coaching staff that he will opt out and begin preparing for the NFL draft.