After trailing most of the game, Brown converted a free throw with 1:17 remaining to cap a 10-2 Missouri (23-11) run and give the Tigers an 81-74 lead. Davidson's Tyler Kalinoski hit a 3-pointer to end the streak, but the Wildcats could get no closer than four points the rest of the way.
With the win, Missouri advances to face the winner of Wednesday's matchup between Southern Mississippi and Toledo.
De'Mon Brooks led Davidson (20-13) with a career-high 29 points. The Wildcats ended their season with two consecutive losses after winning 13 in a row to win the Southern Conference regular-season title.