Lehigh (13-14, 6-8 Patriot League) closed within 63-60 with 4:10 left, and then both teams went scoreless until Justin Burrell's 17-foot jumper with 30 seconds to go put Holy Cross (16-10, 10-4) up by five.
Lehigh scored quick layups on its next two possessions, but Burrell answered each time with two free throws to extend the Holy Cross lead back to five.
After Mackey McKnight missed a 3-pointer for Lehigh with 12 seconds left, Holy Cross claimed the ninth win in its last 10 games.
The Crusaders never trailed and jumped ahead 30-19. But the Mountain Hawks answered with eight straight points and stayed within striking distance from there.