Jean-Paul Olukemi and Keiton Page each scored 19 for the Cowboys (15-7, 3-5 Big 12), who ended a three-game losing streak.
Missouri (17-5, 3-4) lost its fourth consecutive league road game after arriving in Stillwater just six hours prior to tip-off due to travel issues. Marcus Denmon and Matt Pressey each scored 15 points to lead the Tigers. Ricardo Ratliffe added 13 before fouling out.
OSU, which led by 15 with 10 minutes to play, hit 29 of 43 from the foul line, including a big pair by Olukemi with 1:33 to play that gave the hosts a 73-67 advantage.
Pressey's 3 cut the deficit to 73-70 in the final minute but Olukemi hit two more that helped push the margin back to 76-70.