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.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.