Barbour also had six assists for the Lions (7-5), giving the senior guard 301 for his career and tying Mike Jelinsky (1989-93) on the school’s all-time list.
Steve Frankoski’s 3-pointer with 4:41 remaining put Columbia ahead to stay, 56-54. The Lions took a 60-56 lead on Mark Cisco’s jumper, with an assist from Barbour, and Barbour’s jumper made it 62-56 with 2:26 remaining.
Columbia led 30-22 with 1:49 left in the first half, but the Raiders (5-10) went on a 14-0 run, spanning halftime, to go ahead 36-30.
Murphy Burnatowski, John Brandenburg and Pat Moore each scored 13 points to pace Colgate, which had won its last two games.
Frankoski finished with 11 points for Columbia, which turned the ball over just seven times.