Donte Thomas scored and Carter hit another 3 to tie it at 63. The teams traded baskets before Thomas' layup gave the Red Wolves their last lead of the game at 67-65. Taylor's layup tied it and Kedar Edwards' jumper put Tennessee Martin (5-7) up with 1:04 left.
The Redwolves shot 1 for 4 the rest of the way.
Edwards and Taylor each had six offensive rebounds as Tennessee Martin had 22 boards at the offensive end.
Arkansas State (3-7) was led by Nouhoum Bocoum who scored 16 points and had nine rebounds. Thomas scored 15 points with nine boards.