The Tigers had climbed into the second spot in the national rankings by downing Baylor on the road last weekend, but they wilted down the stretch against an Oklahoma State team that shot 59 percent from the floor.
Missouri had a two-point advantage with 4 minutes to play, but was outscored the rest of the way 17-8.
Nash scored 27 points, hitting three 3-pointers overall, and Brian Williams added 22 points.
The Cowboys (10-10, 3-4 Big 12 Conference) had lost three in a row. One of those setbacks was a 41-point loss to Baylor.
The only other stumble of the season for Missouri (18-2, 5-2) came against Kansas State on Jan. 7. The Tigers had won their first 14 games of the season before falling to the Wildcats.
Ricardo Ratliffe led Missouri with 25 points.