The Coyotes are off to their second 3-0 start in the last four seasons.
Stanley Umude made a pair of free throws with 18:16 remaining for a 50-48 advantage and South Dakota led the rest of the way. Two minutes later his 3-pointer made it a 60-50 contest.
With 27 seconds to go, Rod Melton Jr.'s layup brought Florida A&M within 85-80. Melton missed the foul shot and a chance for a three-point play. On the other end, Hunter Goodrick missed a pair of foul shots and a chance to extend the lead. Then Kamron Reaves missed a jumper for the Rattlers with 19 seconds to play.
Reaves fouled Simpson with 11 seconds to go, and he proceeded to miss both free throws. Melton then made a layup to make it 85-82 with seven seconds left, but he also missed a chance for a three-point play after being fouled. On the miss Bryce Moragne secured the offensive rebound, threw the ball to Reaves, but Kruz Perrott-Hunt blocked his shot attempt to end the game.
Melton led Florida A&M (0-4) with 27 points.