Jesse Chuku scored twice inside the first two minutes and Price hit a pair of 3s as Lehigh (5-12, 3-3 Patriot League) jumped to a 10-2 lead and never trailed.
The Mountain Hawks had a hot game, shooting 62 percent in the first half, leading 40-31 at the break, and finishing 33 of 59 for 56 percent field-goal shooting.
Lehigh held a 39-24 edge in rebounding with all five starters gathering at least six boards. Kyle Leufroy grabbed a career-high nine rebounds to go with 13 points. Price scored 22 with a season-best six treys (Chuku has made five twice). Kempton added 20 points.
Matt Husek, a 6-foot-11 junior, was first off the bench and led Holy Cross (7-10, 2-4) with a career-high 23 points.