The game was a battle for seeding in next week's Big 12 tournament. Winning at K-State for the first time since 2012, Oklahoma (17-14, 7-11 Big 12) earned the #7 seed, gaining a first-round bye, and will face the #2 seed Thursday night.
The Sooners enter the postseason having won three consecutive games after losing 11 of their previous 13 games.
The Wildcats (14-16, 6-12) are the #8 seed and will face ninth-seeded West Virginia in the opening round on Wednesday.
Kansas State has lost five consecutive games.
Gibson dominated early, scoring 12 of Oklahoma's first 15 points as the Sooners built a 15-7 lead in the first six minutes.
But after that initial burst, the game tightened back up, with 10 lead changes and seven ties the rest of the way.
After Kansas State's response to Oklahoma's early run, neither team led by more than five points until less than eight minutes remained.
The Sooners took the lead for good with a 7-0 run for a 52-47 lead just shy of the midpoint of the second half, then steadily stretched the lead to 11.
After scoring 20 points in the first half, Gibson didn't score in the second half until his 3-pointer with 4:27 left put Oklahoma up 70-59.
Gibson was 9 of 14 from the floor with seven of Oklahoma's 11 3-pointers.
Until Gibson got going again late, Tanner Groves carried the Sooners in the second half, scoring 9 of his 14 points after the break.
The Sooners shot 52.8% from the floor, outrebounded the Wildcats 37-22, and made things difficult for Wildcats' leading scorer Nijel Pack.
Pack scored just 10 points, tying his second-lowest scoring output of the season. Mark Smith led Kansas State with 22 points while Mike McGuirl added 21.
Oklahoma scored 20 points on 14 Wildcats' turnovers.