The Trojans (20-10) sank four consecutive free throws over the final 7 seconds after struggling at the line most of the game. Their fifth straight win moved the West Division champions into the semifinals against either Western Kentucky or North Texas.
Moore and De'Andre Eggins both went 2-for-2 from the line after that for the Trojans, who made just 14-of-32 attempts in the game.
Moore made three 3-pointers and had five assists and three steals.
Florida Atlantic finished the season 4-14 in games away from home.