Burrell was 3 for 3 and Beans 4 for 6 from long range for the Crusaders (6-4), who never trailed and led 31-22 at halftime.
After Holy Cross expanded the lead to 14 points, the Big Green (2-5) closed to 47-43 with 8:09 left on a Jvonte Brooks layup.
Burrell answered with a 3-pointer, then Brooks made another layup. After Beans and Dartmouth's Alex Mitola exchanged 3-pointers, Dave Dudzinski scored four straight points as part of a 10-2 run to make it 63-50.
The Crusaders were 15 of 19 from the free-throw line while Dartmouth was only 7 of 16.
Burrell hit 6 of 6 foul shots, making him 25 of 26 for the season.
Brooks finished with 16 points and Mitola 15 for the Big Green.