Malachi Alexander had nine points and 10 rebounds for the Crusaders (11-13, 6-8 Patriot League) who shot 36.2 percent from the field overall and 56.5 percent from the free throw line.
Holy Cross took an early 14-5 lead on a Miller dunk and had a 30-18 advantage at the break.
A De'Vaughn Reid layup early in the second half sparked a 14-6 Holy Cross run to put the Crusaders up 45-29 with 10:22 to play. Austin Price sank a 3-pointer with five seconds left to bring the Mountain Hawks (14-11, 8-6) to within four points, 56-52, before Miller sealed with Crusaders' win with a pair of free throws.
Tim Kempton led Lehigh with 22 points and 11 rebounds.