After Mackey McKnight missed two foul shots, the Bison trailed 78-77 and had a chance to take the lead, but couldn't get the ball into leading scorer Mike Muscala.
McCollum and Jordan Hamilton each hit two foul shots in the final 4 seconds, and Lehigh (26-7) began celebrating after clinching its second trip to the NCAA tournament in three seasons.
This one will be especially sweet for Lehigh after beating Bucknell (24-9) on its home floor. Lehigh rarely flinched behind league player of the year McCollum, who hit an array of tough shots to help withstand Bucknell's second-half rally from an 11-point deficit.
Muscala finished with 30 points for Bucknell.