Dudzinski was 10-for-14 shooting and made all nine free-throw attempts while Burrell, a 5-foot-9 sophomore, converted 9 of 13 shots from the floor and 9 of 10 free throws.
Holy Cross (8-7) shot 51 percent (26 of 51) from the field, made 20 of 22 free throws and hit a season-high 55 percent (6 of 11) from 3-point range.
There were five ties and 10 lead changes before Cullen Hamilton broke open a 25-all game with a free throw. Burrell then scored Holy Cross' last eight points of the half to put the Crusaders up 34-25 lead at intermission.
Grant Mullins had 16 points for Columbia (8-6), which never got closer than eight after the break.
Leaving early for the NBA is a risky decision. Some players -- Skal Labissiere, Dejounte Murray -- slid in the draft. Some -- Isaiah Taylor, Troy Williams -- weren't drafted at all.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?
The Tar Heels could lose Justin Jackson and Kennedy Meeks after next season. Coach Roy Williams has nearly every top-10 2017 prospect on his board.