Wesley Person made three free throws after getting fouled on a 3-point attempt to put Troy up 73-69 with 4:59 left. But Arkansas State proceeded to outscore Troy 15-8 the rest of the way.
Devin Carter's layup with 42 seconds left gave the Red Wolves the lead for good at 79-78.
Thomas added two free throws at the 17-second mark, but Person answered with two free throws with eight seconds left to pull Troy to 81-80.
Josh Pierre and Thomas made 3 of 4 free throws for a four-point lead before Person made one free throw before the buzzer.
Arkansas State (5-7) got 15 points apiece from Carter and Anthony Livingston, who also collected 12 rebounds.
Person led the way for Troy (5-7) with 20 points.