Arkansas State fell behind by 18 points with 8:30 to go in the first half and fought its way all the way back to force an extra period.
Daniel Bryant had two foul shots for the Red Wolves with 35 seconds left in regulation but could make only one of them to leave the game tied at 65-65. Chris Crawford missed his attempt at a game-winner for Memphis with 4 seconds left in the second half.
Arkansas State took an early four-point lead in overtime but two free throws by Charles Carmouche put the Tigers in front for good at 71-69 with 2:10 left.
Will Barton scored 20 points for the Tigers (6-0) and Wesley Witherspoon had 12.
The Red Wolves were led by 16 points from Bryant. Arkansas State has won just once in seven games this season, that victory having come in its previous outing against Southeast Missouri State.