Smith scored seven straight Indiana State points late in the second half, capped by a 3-point play, for a 61-52 lead.
Brown added 15 points on 9-of-10 shooting at the line for Indiana State (12-9, 6-3 Missouri Valley Conference). Brenton Scott had 10 points and Brandon Murphy grabbed 10 rebounds - seven on the offensive end.
Both teams struggled from the floor, shooting below 38 percent. Indiana State made just 9 of 33 attempts (27 percent) in the first half but hit 47 percent in the second.
Dixon led Missouri State (8-13, 4-5) with 19 points and Dequon Miller added 12.