The Huskers (8-3, 5-2) clinched the North Division with their fourth straight win and will play South champion Texas on Dec. 5 for the conference title and a BCS bowl bid.
"We've steadily improved and we've hung together," Nebraska coach Bo Pelini said. "We were in a tough spot after the Iowa State game, and everybody wanted to write us off. There's too much character in the locker room."
Nebraska will go to the Big 12 title game for the first time since 2006 and fifth time in the league's 14 years. First, though, the Huskers travel to Colorado to finish the regular season Friday.
"There's not going to be any patting ourselves on the back," Pelini said. "That's for another time. We enjoy this win tonight and then get back to work."
Roy Helu Jr. ran 26 times for 95 yards and a touchdown and went over 1,000 yards for the season, and Zac Lee completed 13 of 19 passes for 166 yards and a score. Nebraska's defense did the rest, holding Kansas State scoreless after the game's opening series.
The Wildcats (6-6, 4-4), who would have won the North with a win, ended their season with losses in three of their last four games. Because two of their wins were against lower-division teams, they needed to beat Nebraska to become eligible for a bowl game.
"We made some mistakes that cost a very fine opportunity for our program, our players and our seniors," said K-State coach Bill Snyder, who came out of a three-year retirement to return to the Wildcats' sideline. "I was saddened that we couldn't deliver on that opportunity, but I was proud of our football team for putting themselves in the position they were in this evening."
Nebraska rebounded to win the division after losing two of its first three games in Big 12 play. Back-to-back home losses to Texas Tech and Iowa State started a stretch of four games in which the Huskers scored a total of four offensive touchdowns.
But the Huskers tweaked their offense, installing the power-I formation and using less of the spread. They also overcame a quarterback controversy that saw freshman Cody Green start two games before Lee regained control of the job two weeks ago.
"We're a true team. We're together, and we're with the process," Lee said. "We know what we have to do, and we don't care what it is as long as we win."
Helu, who has 1,057 yards despite missing lots of time because of a shoulder problem in October, gave the Huskers a two-touchdown lead early in the third quarter with his 14-yard run.
"We knew we couldn't let them hang around and be within one touchdown of us," center Jacob Hickman said. "We knew the best way was to come out after half and just score. We ran the ball a little, passed the ball a little and got it in there."
Big 12 rushing leader Daniel Thomas ran 19 times for 99 yards for Kansas State, and Grant Gregory was 11 of 31 for 126 yards. But the Wildcats failed to score a touchdown for the second straight game despite their offense spending most of the second half on Nebraska's side of the 50.
"In the Big 12 you have to score touchdowns to win games," said kick return phenom Brandon Banks, who was held mostly in check. "We left a lot of points on the field."
The Wildcats, trailing by two touchdowns, drove to the Nebraska 25 in the last 4 minutes, but Ndamukong Suh and Barry Turner teamed up to sack Gregory and the Wildcats turned the ball over on downs when Gregory led Banks too much on a ball thrown toward the end zone.
The Huskers took over with 3:41 left and were able to run out the clock after Lee sneaked for a first down on fourth-and-1 from his own 36.
"We just went in there and said we're going to get this. We're going to end this game right here and go to Dallas," Hickman said.
Kansas State's only points came on the game's opening series, when Cherry kicked a 44-yard field goal.
Nebraska settled for Alex Henery's 34-yard field goal after Lee overthrew Mike McNeill in the corner of the end zone on the Huskers' opening possession.
Lee hooked up with McNeill the next time the Huskers had the ball to put Nebraska up 10-3. McNeill slipped open and snagged the high pass over the middle for a 17-yard touchdown.
"We're definitely happy with the situation we're in," Suh said. "We accomplished our main goal, getting to Dallas. But if we want to dominate the North, we have to go out to Colorado and take care of business."