The Trojans, who won their fourth straight, had 563 yards of offense, including 391 by Brown.
Brown was 28-for-37 and threw consecutive touchdown passes in a 21-point second quarter for Troy (4-2, 3-0 Sun Belt Conference).
Brown connected with Jerrel Jernigan for 40 yards and the first of three-straight TDs for the Trojans in the third quarter.
Jernigan finished with 97 yards on five catches.
DuJuan Harris had 86 yards on 18 carries for Troy, who trailed 10-7 before the 21-point outburst.
Florida International (1-5, 1-2) was led by Paul McCall with 257 yards, two touchdowns and an interception on 27-of-48 passing.
McCall threw a 2-yard TD pass to Jason Frierson as time expired to cut Troy's lead to nine.