Jack Isenbarger scored 14 points for the Phoenix (5-2), who matched their best start since the 1996-97 season.
Elon has held opponents in each of its five wins to less than 40 percent field goal shooting. The Midshipmen (3-6) shot 27.5 percent) from the field and made only 4 of 21 attempts from 3-point range.
The Phoenix did not fare much better, shooting 33.3 percent (17 of 51) from the field and made only 7 of 24 in the first half.
Neither team led by more than four points in the second half and there were 10 ties.
J.J. Avila scored 14 points to lead Navy (3-6), which has failed to score 50 points in each of its past two games.