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.
Sparkling facilities are one thing, but Tim Miles needs to regain the momentum of Nebraska's 2014 run to the NCAAs if it is to play with the big boys.
Oregon finished on top of the Pac-12 last season and made a run to the Elite Eight. With loads of talent returning, will the Ducks continue their reign?
Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.