The Tigers (24-1, 12-0), who kept a number of streaks alive, have won 17 straight games, 26 in a row in the conference, 10 straight over Columbia and their last 44 in the month of February.
Just as they did in their first meeting, the Lions (11-14, 6-7) kept it close for a while, trailing 18-17 at halftime and 34-28 with 10:38 to play.
It was 45-35 with 4:39 left, but Columbia managed only two points after that.
Princeton has won all its Ivy league games by at least 11 points
the first meeting with Columbia was a 58-45 victory and by an average of over 23 points.
Combined with Penn's 73-70 loss to Cornell, the Tigers became the first team to earn an automatic berth in the NCAA tournament's field of 64.
Tigers center Steve Goodrich scored seven points in a 10-3 run to open the second half, but was saddled by foul trouble throughout and finished with 11 points.
A 3-pointer by Justin Namolik pulled the Lions, who had won four straight games, to 34-28, but a 9-2 run gave Princeton a 43-30 lead with 6:44 left.
Princeton sealed it with a 6-0 run that made it 51-35, the largest lead of the game, with 1:41 to play.
Gary Raimondo had 13 points for Columbia, while Namolik added 12.
Brian Earl also had 11 points for Princeton, which shot 6-for-25 in the first half (24 percent), including 4-for-15 from 3-point range. Columbia wasn't much better, shooting 31.8 percent (7-for-22), including 1-for-5 from beyond the arc.
Princeton was the first Top Ten team to visit Levien Gym since then-No. 1 St. John's beat the Lions there on Feb. 12, 1985.
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