American (13-7, 9-0 Patriot League) closed the first half by scoring 16 of the last 17 points and took a 37-17 advantage into the break.
The Eagles made 18 of 20 second-half free throws and finished the game 21-of-39 (53.8 percent) from the floor. They out-rebounded Navy 35-22.
Zach Fong led Navy (7-13, 2-7) with 11 points. The Midshipmen shot just 37 percent (17 of 46) from the floor and 59 percent (13 of 22) from the free throw line.
The Eagles registered 16 assists on 21 field goals.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.