Thomas scored 15 points with nine rebounds and Devin Mitchell made five 3-pointers for his 15 points for the Panthers (14-4, 5-0 Sun Belt).
Kane Williams gave Georgia State the lead with two free throws with 1:09 remaining and Thomas hit a 3-pointer 30 seconds later and added a free throw.
South Alabama had three shots at a tying 3-pointer in the final six seconds.
Georgia State led by six at halftime and went up by 11 with 17 minutes to go after a 9-0 run. Ajayi scored four straight points to give the Jaguars their only lead of the second half with 1:39 remaining.
Oliver dunks it for TBT game-winner
Devin Oliver flushes the putback dunk giving the Red Scare an 80-78 win in The Basketball Tournament.
Ex-Baylor star Austin scores 14 in debut at TBT
Isaiah Austin made his American professional debut, scoring 14 points in Friday's opener of The Basketball Tournament.
TBT 2019 schedule, tip times, TV info, expert picks
The $2 million TBT begins on Friday. Here's info on how to watch and who our experts are picking to win The Basketball Tournament.