It was the first meeting with a ranked foe this season for the Orangemen (11-1), who opened a double-digit lead early in the second half and used timely shooting to hold off the Tigers.
Freshman Gerry McNamara scored 14 points and hit a pair of key 3-pointers after Missouri used a 9-0 run to close within 61-57 with just over eight minutes to play.
Ricky Clemons scored 26 points and Arthur Johnson added 17 points and 11 rebounds for the Tigers (10-2), who had a four-game winning streak snapped.
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