Brown's trey with 55.1 seconds remaining gave Missouri a 63-62 lead.
The Wolfpack's Anthony Barber went to the foul line with 26.8 seconds to go but missed the front end of a 1-and-1, and Missouri's Earnest Ross grabbed the rebound.
Jordan Clarkson then connected on a pair of foul shots for a 3-point Tigers lead with with 20.1 seconds left and Tony Criswell followed with two more free throws to seal the win for Missouri (11-1).
Clarkson finished with 21 points and Brown added 17 for the Tigers.
T.J. Warren led North Carolina State (9-3) with 24 points and 13 rebounds.