C.J. McCollum added 15 points, Jordan Hamilton 13 and B.J. Bailey 10 for the Mountain Hawks (24-7). Lehigh now moves on to play American University, which beat Army in another quarterfinal game, at home in the semifinals on Saturday.
The Mountain Hawks led most of the way, taking a 33-26 advantage at intermission and outscoring the Raiders 37-31 to seal it in the second half.
The Raiders outshot the Mountain Hawks 41.3 percent (19 of 46) to 38.1 percent (24 of 63) from the floor and outrebounded them 39-32, but Colgate also committed 22 turnovers. Lehigh, which tallied 13 steals in the contest, gave it away just nine times.
Sterling Melville scored 21 points to pace Colgate (8-22).