Austin Morgan added 14 points, including six free throws in the final 1:56, as the Bulldogs (18-7, 8-3) remained two games behind Harvard and a half-game behind Pennsylvania in the conference race.
Yale never trailed, leading by as many as 15 points in the first half and 47-36 with 13:25 remaining. The Lions (14-13, 3-8) battled back for a 56-56 tie with 6:06 to go, before Yale went ahead to stay on two free throws and a jumper by Brandon Sherrod that made it 62-58 with 4:05 left.
The Bulldogs have won their last seven games against Columbia.
Brian Barbour scored 21 points and handed out eight assists for the Lions, who also got 13 points from Alex Rosenberg.