AMES, Iowa — Todd Reesing threw for 319 yards and three touchdowns, and No. 16 Kansas stormed back from a 20-point hole before hanging on to beat Iowa State 35-33 today.

Kerry Meier caught seven passes for 125 yards and two TDs for the Jayhawks (4-1, 1-0 Big 12), who tied the third-biggest comeback in school history by outscoring the Cyclones 35-13 in the second half.

It wasn't easy, though.

Cyclones freshman Sedrick Johnson followed a late Iowa State touchdown by recovering an onside kick with 1:13 left, giving the Cyclones the ball at their own 41. But the Jayhawks defense clamped down, forcing Iowa State's Austen Arnaud to throw four straight incompletions.

Arnaud threw for a career-high 268 yards and three touchdowns for Iowa State (2-3, 0-1), which blew a golden opportunity for its first win over a ranked team since 2005.

The Jayhawks' comeback was their biggest since 1992, when they rallied from 26 down to beat the Cyclones 50-47.

Kansas flexed its big-play muscle in the third quarter, scoring touchdowns on three straight possessions to move ahead 21-20.

Reesing found a wide-open Jake Sharp, who sneaked out of the backfield and into the flat, and he went 67 yards for the Jayhawks' first TD. Sharp got the next drive started by taking a shovel pass 42 yards, and Angus Quigley followed Reesing's third-down scramble with a 1-yard touchdown run midway through the third quarter.

Kansas then gambled on fourth-and-6 at the Iowa State 23. Reesing dashed outside the pocket and hit Meier in stride for the go-ahead touchdown with 1:46 left in the third quarter.

Kansas appeared to deliver a crushing blow early in the fourth when defensive lineman Maxwell Onyebule picked off Arnaud and returned it to the Iowa State 6. Sharp, who also caught a touchdown pass, scored from 2 yards out to make it 28-20 with 9:23 left.

But Arnaud found R.J. Sumrall for a 22-yard touchdown pass less than 2 minutes later, and after Arnaud's conversion pass fell incomplete, Kansas still led 28-26.

The Jayhawks went 80 yards in eight plays and went ahead 35-26 on a 21-yard TD pass from Reesing to Meier with 3:39 left. Iowa State responded for the second time that quarter, with Arnaud hitting Marquis Hamilton for a 2-yard TD with 1:15 left.

The Jayhawks hadn't allowed any points in the first quarter through four games, but it took just 11 minutes for the Cyclones to jump ahead 14-0.

Iowa State's first drive went 55 yards in five plays, as Alexander Robinson burst through a huge hole up the middle for a 16-yard touchdown. After Kansas stalled deep in Iowa State territory, Arnaud found Hamilton for an 8-yard score with 3:56 left in the first quarter.

The Jayhawks went three-and-out on their first three drives, for zero net yards.

Then it got worse.

Iowa State recovered a fumble on the Jayhawks 42, and Grant Mahoney's 31-yard field goal gave the Cyclones a 17-0 lead with 12:25 left in the half. Reesing then tried his luck deep, but freshman Leonard Johnson jumped the route for an interception at the 50.

Mahoney added a 43-yarder into a stiff wind to make it 20-0 midway through the second.