Jake Odum, Jordan Printy and R.J. Mahurin added 10 points apiece for Indiana State (6-1), which is off to its best start since 2005-06 when the Sycamores opened the season by winning eight games in a row. Odum also had 12 assists.
Fairfield (3-4) got 21 points from Rakim Sanders, who averaged 19 points in the Stags' first two tournament games.
Odum's driving layup 2 1/2 minutes into the second half extended Indiana State's lead to 43-27. Lathan had a layup, off a nifty pass by Odum during a three-on-one, to make it 53-35 with 11:42 to play.
Sanders made a basket and hit two free throws in the final minute of play to get Fairfield within 69-66.
Lathan made two free throws with 21 seconds left to make it 71-66.