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.
Nike Men's Iowa State Cyclones Cardinal Football Icon Legend T-ShirtShop
Despite battling the flu all week, Will Grier will start at quarterback for No. 25 Florida on Saturday when the Gators host No. 3 Ole Miss.
Florida State running back Dalvin Cook exited with a left leg injury in the first quarter of the Seminoles' 24-16 win over Wake Forest and did not return. He is day-to-day, Jimbo Fisher said.
Trevone Boykin threw five touchdown passes, including four to freshman KaVontae Turpin, and No. 4 TCU rode a 30-point first quarter to a 50-7 rout of Texas on Saturday.
As if things weren't going bad enough at Texas, the Longhorns appear to have players on Twitter during lopsided losses and jabs at their coach accidentally being sent from other nearby teams.
Tulane long-snapper Aaron Golub became the first legally blind person to play in a Division I football game Saturday, according to the school.
LJ Scott ran for 146 yards and two touchdowns, and No. 2 Michigan State held on through a lackluster second half to beat Purdue 24-21 on Saturday.