Lehigh (16-14, 10-8) held a narrow 27-23 lead at intermission, but the Eagles shot 7 of 10 in the first five minutes of the second half to pull ahead. A 3-pointer from Reed stretched their lead to 10 with 4:29 left.
The Mountain Hawks threatened with 57 seconds remaining after Jesse Chuku's jumper made it a two-point game. American shot 5 of 6 from the line in the final 45 seconds to stay ahead.
Tim Kempton led the Mountain Hawks with 20 points and 11 rebounds.