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.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.