Josh Davenport converted a pair of free throws to give Winthrop a five-point lead, 61-56, with 4:09 left, but Lester Wilson drilled a 3-pointer and Rashawn Rembert converted a pair of free throws to even the game at 61-61 with 2:31 left.
Riley gave ETSU the lead on a 3-pointer with :50 seconds left and, after A.J. Merriweather added the second of two free throws, Riley added four straight free throws, the final pair with :03 left.
Wilson finished with 20 points to lead the Buccaneers (3-1) and Rembert added another 16. Riley contributed 10 points off the bench.
Moore finished with 24 points to lead Winthrop (2-2), with Andre Smith adding 12 points off the bench.