Oklahoma State saw Kansas tie the game in the fourth quarter before their most exciting player made the difference-making play in a 27-20 win in Lawrence, Kansas, on Saturday.
The Cowboys' first possession appeared to end in an interception by Kansas' Matthew Boateng, but the call was overturned on replay review.
OSU's second possession featured a 24-yard pass from Daxx Garman to David Glidden, which set up a 43-yard field goal by Ben Grogan to go up 3-0.
Kansas answered by going 75 yards in 10 plays, with Michael Cummings going deep to Nick Harwell for a gain of 51.
That set up a one-yard touchdown run by Cummings to give the Jayhawks a 7-3 lead with 5:10 to play in the first quarter.
KU had a poor kick on the ensuing kickoff, giving OSU the ball at the Jayhawks' 48-yard line.
It took the Cowboys just five plays to score, with Desmond Roland going 33 yards for a touchdown to give OSU the lead back at 10-7 with 3:48 to play in the first quarter.
Roland had 87 yards rushing on 21 carries.
OSU got the ball late in the first quarter and marched to a field goal in the second quarter, with Grogan kicking a 24-yarder to make it 13-7 Cowboys with 10:55 to play in the first half.
Oklahoma State appeared to be on their way to extending the lead when Garman found Tyreek Hill for a gain of 38, with Hill taking a big hit just after he caught it.
The Cowboys had to settle for a field goal attempt, but Grogan's 33-yarder was deflected by Tevin Shaw and missed wide left.
Kansas couldn't do anything with it on offense, though, and a shanked punt gave OSU the the ball at the KU 30.
The Cowboys converted, with Garman passing in the right corner of the end zone to Jhajuan Seales, who made a leaping catch for a 7-yard touchdown to make it 20-7 Cowboys with just 26 seconds left in the first half.
Garman was 17 for 31 passing for 161 yards with one touchdown and one interception.
Early in the second half, Kansas forced a Cowboy turnover, as Cassius Sendish intercepted a deep pass by Garman and returned it 29 yards to the Kansas 37.
The Jayhawks couldn't do anything with it, however and had to punt.
Kansas kicker Matthew Wyman missed a 42-yard field goal attempt later in the third quarter and OSU took over possession.
On the next play, Michael Reynolds hit Garman just as he was throwing it, and the ball went forward, apparently incomplete.
Officials never blew the whitle, and the play was ruled a fumble, as Tevin Shaw scooped it up and returned it to the OSU 15.
Kansas had to settle for a 21-yard field goal by Wyman to make it 20-10 with 3:08 left in the third quarter.
The Jayhawks trimmed the lead even more early in the fourth quarter when Corey Avery scored on a 23-yard touchdown run to make it 20-17 with 14:13 to play in the fourth quarter.
OSU got a first down on a facemask penalty, but then had to punt after three downs, and Kansas marched to a tying field goal.
On 4th and 2, the Jayhawks picked up a first down when Cummings passed to Avery for 16 yards.
KU's drive bogged down at the 17-yard line and they settled for a 35-yard field goal from Wyman to tie the game at 20 with 6:55 to play.
OSU's answer was immediate and impressive, as Tyreek Hill returned the ensuing kickoff 98 yards for a touchdown to put the Cowboys back on top 27-20 with 6:43 to play.
Hill finished with 170 all-purpose yards.
The two teams exchanged punts, then Kansas took over with 2:04 to play and no timeouts.
With 1:08 to play on 4th and 12, Josh Furman intercepted Cummings to seal the Cowboys' 5th straight win.
Kansas finished with more than 100 yards of total offense more than OSU, 379-275.
OSU improves to 5-1, 3-0 in Big 12 play, while Kansas drops to 2-4, 0-3 in conference play.
The Cowboys visit TCU next Saturday at 3:00.