Hicks' jumper with 2:18 left gave the Quakers (8-18, 3-9 Ivy) a 44-35 lead with 2:18 to play. From there they made 8 of 9 free throws along with Matt Howard's layup at the 41-second mark to secure the win.
Penn used a 17-1 run to lead 23-6 near the end of the first half while Columbia (13-14, 5-8) went 13:25 without a field goal. Luke Petrasek's 3-pointer with 40 seconds left gave the Lions nine points at halftime.
The Quakers matched their largest lead midway through the second half at 38-21 before Columbia scored 11 straight, but Columbia got no closer than six points the rest of the way.
Sam Jones added 14 points for Penn.
Maodo Lo scored 21 to lead the Lions.