The Mountain Hawks (19-7, 7-3 Patriot League) trailed 46-40 at halftime, after allowing the Raiders to shoot 68 percent in the first half (17 of 25).
Lehigh then shot 70.8 percent from the field in the second half (17 of 24) and outscored the Raiders 49-23 in the final 20 minutes.
Lehigh led 65-61 with 11:03 remaining and blew it open with 19 straight points. Knutson scored eight during the spurt and McCollum capped it on a layup with 4:28 left.
Colgate missed all 11 of its shots during the spurt.
Lehigh scored 21 points off 13 turnovers and outrebounded the Raiders 33-22. McCollum led the Mountain Hawks with 10 boards.