Murray State (20-6, 12-3 Ohio Valley Conference) has won eight straight and sent the Gamecocks (5-22, 3-13) to their fourth loss in five games.
Miles finished with 13 points for the Racers, including hitting both of his foul shots for a 60-56 lead, giving the Racers enough cushion to withstand B.J. Miller's 3-pointer with 2 seconds left.
Jacksonville State led until Miles hit a 3-pointer for a 46-45 lead with 7:17 to play. Murray State led the rest of the way, but never more than seven points.
Murray State shot 57.1 percent from the field (12 of 21) in the second half.
Brian Williams scored 16 points, Stephen Hall had 14, Miller added 11 and Nick Murphy had 11 rebounds for the Gamecocks.