Kempton, who had 28 points in a loss to Army on Wednesday after missing three games due to injury, turned in his third double-double this season and 23rd of his career.
Kyle Leufroy added four 3-pointers and 20 points for the Mountain Hawks (3-10, 1-1 Patriot) while Austin Price had three treys and 16 points. Lehigh was 10 of 17 from 3-point range for 59 percent, better than their 45 percent overall.
Nathan Dieudonne had 17 points and John Papale 13 for the Terriers (7-8, 0-2) while Nick Havener added 13 points and 11 rebounds for his third double-double.
Lehigh led by one with 4:29 to go when the Hawks went on a 10-2 run for a 73-64 advantage with two minutes left. Eight free throws from there kept BU at bay.