Price made 10 of 15 field goals, grabbed eight rebounds and had three steals.
Jesse Chuku added 13 points, including three 3-pointers, and Tim Kempton scored 11 for Lehigh (6-13, 4-4 Patriot League), which hit 10 3-pointers.
Chuku and Tyler Jenkins hit two 3s apiece during a 14-6 run that made it 29-21 with 7:13 left in the first half and the Mountain Hawks took a 40-33 lead into the break.
Back-to-back 3-pointers by Austin Tillotson and Jordan Swoopshire pulled Colgate (10-10, 6-3) within three midway through the second half, but Price answered with a pair of 3s to start a 10-0 run that made it 63-50 with 7:14 left and the Raiders trailed by at least seven the rest of the way.
Tom Rivard scored 19 and Tillotson 18 to lead Colgate.