Lehigh downed the regular-season champion Bison on their home floor to earn a trip to the NCAA Tournament.
After taking a six-point lead into the final 2 minutes, Lehigh found itself with only a one-point advantage when McCollum was fouled with 4 seconds to go.
He made both free throws and Hamilton promptly stole the ball from Bucknell's Joe Willman. Hamilton's two foul shots wrapped up the victory and boosted the Mountain Hawks to 26-7 for the season.
Lehigh was the tournament's No. 2 seed and will take an eight-game winning streak into the NCAA tourney.
McCollum scored 29 points, making 10-of-13 from the line. Gabe Knutson added 23 points and seven rebounds for Lehigh.
Bucknell (24-9) was led by 30 points and 14 rebounds from Mike Muscala.
The teams split their two regular-season meetings, each winning on the other's court.