Sean McGonagill added 14 points and Halpern finished with eight. Sullivan, who also had six steals, became the 26th Brown player to score 1,000 career points (1,007) and tied the Bears' record for career games played with 115.
Brown (12-14, 6-6) trailed 31-20 at halftime but rallied to tie it 53-all on a McGonagill jumper with 4:19 left. Columbia (12-14, 4-8) then missed its next two shots and two free throws, as Brown went up by four, 57-53, but converted five shots from the charity stripe over the ensuing 2 minutes to knot it at 58.
The Bears called a timeout and Halpern came off the bench to sink the game-winner.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.