Brett Comer had 12 assists, including alley-oop feeds to Morant for his seven dunks, including four in a row. Christian Terrell scored 11 points for the Eagles (10-5), who won their program-record 10th non-conference game of the season (previous record: 8 in 2012-13).
Ave Maria jumped to a 12-5 lead on a 3-pointer by Exor Torres but FGCU used a 12-1 run to close within one and trailed 13-12 at halftime.
FGCU pulled ahead 21-19 on a layup by Terrell, then Morant made four dunks in a row to spark a 16-0 run and the Eagles led 37-22. Later Morant hit three dunks in a row for a 43-31 lead.
Torres led Ave Maria (7-6), an NAIA member, with 12 points and Jelani Bonner had 11.