The Tigers (16-3, 3-1 Big 12) led 91-76 with 4:10 to play but were outscored 19-6 down the stretch. All six of Missouri's points came at the free throw line.
The Cowboys (12-5, 1-2) had at least seven chances to tie or take the lead over the final two minutes but could not convert field goals, including a frenzy under the basket with under five seconds to play.
Obi Muonelo led all scorers with 22 points and pulled down 12 rebounds. Terrel Harris and Byron Eaton each chipped in 21 points and James Anderson added 17.
The Tigers, who were outrebounded 44-42, led 52-42 at the half.
Missouri returns to action 12:30 p.m. Saturday when it will host Texas Tech in a conference game.