With the win, OU halted an eight-game road losing streak in Big 12 play and a stretch in which it had lost 19 of its last 20 conference contests away from Lloyd Noble Center.
It also pulled OU within one victory of its win total all of last year with 10 games remaining in the regular season.
Guard Steven Pledger sparked the start and solid team defense finished it.
Pledger scored 18 first half points on his way to a game-high 31 on 11-for-17 shooting and hit a pair of critical threes that turned a 51-49 deficit into a 55-51 lead just shy of the five minute mark.
OU milked that slim lead into the final minute, and it was 59-58 when point guard Sam Grooms tried to stretch it back to three with a jumper inside the lane.
He came up short and Kansas State snagged the rebound, but with the play of the game, Grooms ripped it away and paved the way for the Sooners to seal it at the foul line.
Grooms and forward Romero Osby went 4-for-4 in the final nine seconds at the charity stripe, and the Wildcats' last second heave clanked off the back iron.
The Sooners, though, had to work harder for it than they wanted to, given they raced out to a double-digit lead early in the second half.
But foul trouble for Pledger and forward Andrew Fitzgerald forced two of OU's starters to the bench.
That set the stage for K-State's rally.
Trailing 40-30 at the 17:29 mark of the second half, the Wildcats rattled off 10 unanswered points to tie it up.
They later led by as much as three twice, at 46-43 and 48-45.
But OU held Kansas State without a field goal for the next three minutes and was able to regain the lead down the stretch.
The Sooners never relinquished it again.
Along with Pledger, forward Cameron Clark finished as the only other Sooner in double figures with his 11 points on 5-of-9 shooting from the field.
But turnovers proved to be the telling statistic, as the Wildcats committed 20 of those to just 14 for the Sooners.
Kansas State, the conference's No. 1 rebounding team, out-boarded OU 33-29.
The Sooners (13-7, 3-5 Big 12) will cap off a two-game road trip when they head to Lawrence, Kan., for an 8 p.m. CT Wednesday contest against the No. 5 Kansas Jayhawks at Allen Fieldhouse.