Reischel was 9 of 9 from the stripe, including two to seal it with 28 seconds left.
Eastern Kentucky opened the second half on a 12-3 run, with seven points from JaVontae Hawkins, for a 49-38 lead. The spurt was highlighted by Nick Mayo's steal and feed to Hawkins for an alley-oop dunk.
Florida Atlantic rallied to within 68-66 but EKU answered with a 6-0 run, capped by Dujuanta Weaver's athletic tip-in of Reischel's missed 3-pointer. Hawkins made it a seven-point game with a minute left on a putback of his own miss.
Mayo added 18 points for Eastern Kentucky (8-4) and Hawkins finished with 15.