Kevin Puryear had 12 points and five rebounds, including 8 points in the second half, and Russell Woods scored 10 points and grabbed eight rebounds, tying a team high.
The Tigers (4-3) held a 10-point lead near the 12-minute mark, but the Hilltoppers whittled it away, mounting a 14-5 run while Missouri missed its final eight field goal attempts.
Pancake Thomas missed a 3-pointer with :04 seconds remaining and Missouri guard Cullen VanLeer secured the rebound before being fouled. He sank two free-throw attempts to extend the Tigers' one-point lead before the Hilltoppers' last-second half-court attempt fell short. Thomas finished with nine points and five rebounds on 3-for-12 shooting.
Western Kentucky (3-5) jumped to an early 9-3 lead while Missouri shot 3-for-13 from the field to start the game.