Florida Atlantic (2-3) trailed American U 55-52 before Jordan McCoy's free throw cut the deficit to two, 55-53, with 59 seconds left to play.
After Stephen Lumpkins missed a jumper for American (2-3) with 28 seconds remaining, Moody answered with the biggest shot of the game.
With 14 seconds left, Jackson Trapp found Moody for the go ahead 3-pointer, 56-55. Moody added two free throws with 2 seconds to play to extend the lead to three, 58-55, but Daniel Munoz missed a game-tying 3 at the buzzer to seal the win for Florida Atlantic.
Moody finished with eight points and six rebounds, and Trapp added 12 points and six assists.
Lumpkins led the Eagles with 17 points.