Brown connected on 5-of-7 shots from beyond the arc while Alex Oriakhi chipped in with 16 points and 10 rebounds for the Tigers (12-2, 1-0 SEC), who played their first-ever SEC game after bolting the Big 12 after last season.
Phil Pressey added a double-double of 11 points and 13 assists as Missouri racked up its eighth straight home victory.
Laurence Bowers left the game in the second half with a knee injury after netting 16 points for the Tigers.
The Crimson Tide (8-6, 0-1) were led by Trevor Releford with 26 points.
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