Down eight with 20 seconds to go, Tilman Dunbar hit a 3 to cut Lehigh's lead to five.
Austin Price made 2 of 4 free throws down the stretch to seal it.
Kempton had 12 points for the Mountain Hawks (14-11, 8-6 Patriot), who converted 20 of 25 free throws.
Worth Smith finished with 19 points, on 8-of-15 shooting, and Dunbar added 13 and six of Navy's 10 assists.
Dunbar made a layup to put Navy up four with 7:32 to go, but Lehigh scored 10-straight points and the Midshipmen (10-16, 6-8) did not score again until 44 seconds left.