Savage scored his second touchdown of the game on a 20-yard run on the second play of the fourth quarter, capping the Cowboys' comeback from an early 16-point deficit. It's the just fourth win for Oklahoma State in 41 games against Nebraska but the second straight for the Cowboys in Stillwater.
Oklahoma State (5-3, 2-2 Big 12) also beat the Cornhuskers 24-21 in 2002, snapping a 24-game losing streak in the series. The loss keeps Nebraska (6-3, 3-2) in a tie for the Big 12 North lead with Missouri, which lost earlier in the day to Oklahoma. Nebraska hosts Missouri next week, with the division title likely on the line.
Nebraska, boasting the nation's seventh-ranked scoring offense, built an early 16-0 lead on the strength of the best half of tailback Brandon Jackson's career.
Jackson ran for 66 yards on six carries to set up Jordan Congdon's 26-yard field goal on Nebraska's opening possession, then was able to finish off each of the Huskers' next two drives with scores from 2 and 24 yards. He had 124 yards by halftime, surpassing his career-high, and finished with 182 yards on 21 carries.
But Oklahoma State, with the nation's No. 11 offense, responded to Jackson's second score by turning the game into a shootout.
The Cowboys got within 16-6 when quarterback Bobby Reid scrambled for 56 yards and then beat Nebraska's blitz with an 18-yard lob to Keith Toston for a touchdown. Jason Ricks, whose extra point try was blocked last week to seal a 34-33 overtime loss to Texas A&M, had his second straight PAT blocked.
The crowd gave a loud cheer when Ricks made the extra point after Oklahoma State's second score, an 18-yard run by Savage, to make it 16-13.
Nebraska answered with Zac Taylor's 22-yard pass to Maurice Purify, who shed Perrish Cox's tackle and tiptoed the final few steps down the left sideline for the touchdown, with 56 seconds left before halftime.
Cox returned the ensuing kickoff 39 yards and Reid hooked up with Adarius Bowman, the nation's No. 2 receiver, for a 45-yard score on the next play.
Neither team got much of anything going in the third quarter, but that all changed on the first play of the fourth quarter.
Reid threw a 55-yard strike to D'Juan Woods on a double move down the left sideline, and Savage ran in from 20 yards on the next play to give the Cowboys a 27-23 lead.
The Cowboys then harassed Taylor, who verbally committed to the Cowboys out of high school, sacking him before consecutive incompletions forced a punt. Oklahoma State responded with a nine-play, 77-yard drive capped by Julius Crosslin's 1-yard dive.
Peterson sealed the game by returning a Taylor fumble 19 yards for a score with 3:16 left, ensuring Oklahoma State would not give up a fourth-quarter lead for the third time in Big 12 play.
Taylor, who had 241 yards and two touchdowns on 21-for-39 passing, moved ahead of Jerry Tagge and 2001 Heisman winner Eric Crouch into second place on Nebraska's all-time passing list with 4,718 career passing yards. His second scoring pass was a 5-yarder to Purify with 7 seconds left.