AMES, Iowa (AP) -Kansas coach Mark Mangino pulled his Jayhawks together at halftime and gave it to them straight. He figured they were bound to start playing better, because they couldn't play any worse.

'''We've played very poorly,''' Mangino said he told his team, which trailed 20-0 at the break. '''But we can win this game, and we will win this game, if you keep your poise, you stay calm.'''

The Jayhawks did just that, answering an awful first half with one of the biggest comebacks in school history.

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 on Saturday.

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.

Iowa State (2-3, 0-1) made the Jayhawks work to the very last minute.

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

Arnaud set career highs with 268 yards passing and three touchdowns, and Iowa State 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.

''Everybody talks about playing for 60 minutes and we haven't done that yet,'' Iowa State second-year coach Gene Chizik said. ''That's really disappointing to me.''

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 in the flat, and the tailback 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.

Sharp, who had been replaced by Quigley as the starting tailback, ran for 79 yards and had 107 yards receiving. He had nine total yards at halftime.

''Jake stepped up and had a huge half, and everybody stepped up offensively and defensively,'' Meier said. ''We felt we needed to establish ourselves, because in the first half we didn't do a whole lot. It was big coming out and getting started early.''

Kansas appeared to deliver a crushing blow early in the fourth when defensive lineman Maxwell Onyegbule 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 two 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, with Arnaud hitting Marquis Hamilton for a 2-yard TD with 1:15 left.

''This is a tough loss for us because we played so in the first half. We came out flat and fought back,'' Iowa State offensive lineman Ben Lamaak said. ''We got the onside kick but we couldn't do anything with it.''

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 on Alexander Robinson 's 16-yard touchdown run and Hamilton's 8-yard TD catch in the first quarter.

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.

The Jayhawks entered halftime facing its biggest deficit of the season. But Mangino's words proved prophetic, because the Jayhawks were a different team in the second half.

''It was atrocious. It wasn't all our fault. They played very well,'' Reesing said. ''We came in the second half and really started clicking on all cylinders and showed what we can do when we're all on the same page.''