The Bison move on to a quarterfinal match with Biola at 6 p.m., Saturday.
OBU shot 39 percent from the field in the first half and despite three fouls on Sooner Athletic Conference co-Player of the Year Emmanuel Wilson and two each on big men Derick Echols and DeAngelo McIntosh, the Bison led 28-24 at the half.
The Bison held Columbia to 34 percent shooting.
"I felt like whoever got it going first in the second half was going to win it," said Bison coach Doug Tolin. "This was a better game for us. I thought we played well on defense all game. We made them work for their shots."
Columbia cut the Bison lead to 30-28 with 17:27 to go, but the Bison turned the game with a 11-0 run with a basket by McIntosh, a free throw by Echols and three-pointers by Heath McKay and Wilson in a span of 3:05.
"We came out firing tonight after being sluggish in the first game," McKay said. "We picked up the pressure on defense and worked hard for rebounds."
The Cougars got as close as seven the rest of the way, but the Bison were able to bulk the lead up to 15 points late and clear the bench.
Wilson, who had seven points before his third foul put him on the bench midway through the first half, finished the game with 24 points and those same three fouls.
McIntosh had 13 points and McKay 12.
The Bison held Columbia big man Jordan Dressler to 16 points and three rebounds after he produced a 20-10 game in the CC tournament opener.
"I thought we made him work," Tolin said. "It was a good night for us, defensively overall."
The Bison out-rebounded the Cougars 36-29.
OBU won its 30th game of the season. It is the 10th 30-win season in Bison basketball history and the seventh for Coach Tolin. The Bison are now 16-4 all-time in second round games at the NAIA Tournament.
The Bison are headed back to the quarterfinals for the first time since 2010 when they won the NAIA title.
OBU (30-4) is 3-0 all-time against Biola, including a 59-54 win in the 2010 tournament.