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.
After a season that saw his shooting numbers slip, should Nigel Hayes return for his senior year at Wisconsin or take the gamble to put him name in this year's NBA draft?
Isaiah Taylor talks about his decision to declare for the NBA draft and what he will miss most about Texas.
Chattanooga women's basketball coach Jim Foster has received a one-year contract extension, the same day the school gave the men's coach a two-year extension.