Army led 59-56 with just under six minutes remaining. But Brown went on a 16-4 run that started and ended with 3-point shots by Sullivan and gave Brown a 72-63 lead they wouldn't lose.
Sullivan was 9-of-15 from the field, including 5-of-9 from 3-point range. Mullery added 17 points and five blocked shots for Brown (2-3).
Simmons led Army (1-4) with 18 points, while Josh Miller scored 16.