STILLWATER, Okla. -- Oklahoma State's offense and defense rose and fell as the telling storylines Saturday, before kicker Ben Grogan settled things by booting the game-winning field goal.

Grogan, who kicked the tying and winning field goals in the final 1:33 the week before, pushed through a 37-yarder with 32 seconds left against Kansas State, rallying the No. 20 Cowboys to a 36-34 victory at Boone Pickens Stadium.

The Wildcats took a 34-33 lead with 3:01 left when quarterback Joe Hubener scored on a fourth-and-three option keeper from the five-yard-line.

But the Cowboys (5-0, 2-0 in the Big 12) marched back down the field, putting Grogan in position to be the hero again after he connected on field goals of 41 and 40 yards in a 30-27 victory over Texas.

"In the end, we found a way to win," said Oklahoma State coach Mike Gundy said. "Ben just goes out and does what he does. Ben was very calm. I think he has a lot of confidence in his ability to make a play."

The Wildcats (3-1, 0-1) led 28-20 in the first half, riding the unexpected play of Kody Cook. The team's fifth-string quarterback was forced into duty when Hubener was knocked out on the game's first series and all other options were either hurt or sick.

Cook, a former walk-on and fifth-year starter at wide receiver, threw for two touchdowns and ran for another.

"I thought he played with poise," Kansas State coach Bill Snyder said. "He played smart. He made some mistakes, but you have to remember we have a plethora of offense and he's had a week of investment in it.

"He was a quarterback some time ago and he's on the field a lot as a receiver, but his retention has been great. He did as well as you could expect."

The Cowboys' defense eventually silenced the Wildcats until Hubener's late touchdown, allowing Oklahoma State to catch up and go ahead -- twice.

Quarterback Mason Rudolph threw for a career-high 437 yards with three touchdowns for the Cowboys. On a day that he completed 34-of-55 passes, his most important throw came on the game-winning drive, when he found wideout Marcell Ateman for 19 yards on fourth-and-eight from the Oklahoma State 37.

"We had them on fourth down," Wildcats linebacker Elijah Lee said. "We just didn't execute."

Soon after, Grogan was kicking another game-winner.

"I feels good to once again be there for my team when they needed me," Grogan said. "The snap and the hold was perfect, and everything just went in my favor."

Cook had last thrown a competitive pass at Hutchinson Community College, when he flipped from receiver to quarterback in a big way, throwing for five touchdowns and running for another as the MVP of the Salt City Bowl.

Joining the Wildcats as a walk-on, he redshirted in 2013, prepping at quarterback and receiver. He played in all 13 games a year ago at receiver, starting 11.

The first half played out as an unexpected shootout, ending with the Wildcats ahead 28-20. For Kansas State, that was courtesy of Cook.

He accounted for all but 45 of the Wildcats' 230 yards of offense, passing for 127 yards and running for 58.

After stepping in for Hubener, Cook continued a march to a touchdown, hitting a key third-down pass play on his first completion to the Cowboys three, and running in from there for a touchdown on the next snap.

If it seemed like a fluke at the time, any such thoughts were soon erased when Cook kept directing impressive drives. He threw two scoring passes -- one to fullback Glenn Gronkowski and another to wideout Deante Burton -- and converted four times on five third downs.

Running back Justin Silmon, a freshman walk-on, scored Kansas State's other touchdown after cornerback Danzel McDaniel picked up a fumbled lateral by the Cowboys and returned it to the Oklahoma State six.

Silmon's touchdown pushed the Wildcats' lead to 28-13.

The Cowboys, as they had much of the half, responded.

Rudolph led an 83-yard drive, capped by his 11-yard throw to wide receiver Marcell Ateman for a touchdown with 46 seconds left.

Rudolph passed for 196 yards and two touchdowns in the half, also connecting with wideout James Washington on a 32-yard scoring play.

Situational quarterback J.W. Walsh threw for Oklahoma State's other touchdown, a four-yard toss to wideout Jalen McCleskey.

NOTES: Kansas State played without starting strong safety Dante Barnett, who hasn't played since the season opener because of a collarbone injury. Barnett, a senior on the Walter Camp and Chuck Bednarik award watch lists, was due a homecoming of sorts after playing at Tulsa's Booker T. Washington High School. ... The Wildcats had won some big road games in the Big 12, including their last two at Oklahoma and three of their five conference trips to Texas, yet haven't won in Stillwater since 1999. ... Kansas State DE Jordan Willis put his hands to good work. In the first half, he broke through to block an extra point attempt after Oklahoma State's second touchdown and batted down a backward pass by Cowboys QB Mason Rudolph, setting up a fumble recovery that led to a touchdown and a 28-13 lead. In the second half, he batted down a third-down pass in Kansas State territory.