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.
Reggie Witherspoon, who spent more than 13 seasons coaching at Buffalo, is returning to the city to coach Canisius College.
North Carolina Hall of Fame men's basketball coach Roy Williams is recovering from knee-replacement surgery.
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.