Holy Cross (10-13, 4-5 Patriot League) jumped out to an early 10-1 lead but Navy rallied to tie the score 24-all at halftime.
The Midshipmen (3-20, 0-9) took a 34-31 lead in the second half behind a Jordan Sugars' 3-pointer. But the advantage was short lived, as the Crusaders used a 16-5 run to go ahead 47-39 with 10:10 left to play.
Beans, who capped the spurt with a layup, had five points during the run and Burrell added a 3-pointer.
Burrell made three 3-pointers and converted on 8 of 10 free throws.
Navy shot just 20 of 52 from the field.
Sugars led the Midshipmen with 20 but no other Navy player scored more than seven points.