Sears blocked Maodo Lo's potentially game-tying 3-point attempt with six seconds left and Matt Townsend made 1 of 2 free throws to seal it for the Bulldogs (14-6, 3-0).
Javier Duren made all four of his free throws in the final 1:06, pushing Yale's lead back to three on each trip. Duren finished with 15.
Yale opened the second half with six straight points and never trailed, but Columbia (9-8, 1-2) hit three consecutive 3-pointers to pull within 58-57 with 3:41 left. Kyle Castlin kept the Lions in contention after his basket pulled them back within one with 26 seconds left.
Lo had 20 points and Castlin added 10 for the Lions, who opened the game leading 11-2 but trailed 35-32 at halftime.