Western Illinois had a two-point lead with 3 minutes to play, then missed six shots from the field and two more from the foul line the rest of the way.
It was the season opener for Missouri, which has won its first game in each of the last five campaigns under Coach Mike Anderson.
Missouri did not have a player in double-figure scoring. Laurence Bowers, Marcus Denmon, Steve Moore and Phil Pressey all had nine points and the Tigers shot just 41 percent from the field.
Matt Lander led the Leathernecks (2-1) with 24 points while Kaimarr Price had 15 points and 12 rebounds.