The Redbirds (15-5, 7-2 Missouri Valley) took a slim 33-28 lead into halftime in a game that was tied four times and in which the lead also changed four times.
The Sycamores (10-9, 5-4 MVC) looked like they might fall by the wayside at several points in the game, but they continued to storm back and keep it close.
With two minutes left, Indiana State tied it up 59-59 on a 3-pointer by Marico Stinson, who scored a game-high 22 points on 4-of-7 shooting from 3-point range.
But Eldridge finally put the game away for Illinois State when he hit a 3-pointer with 37 seconds left.
Other than Odiakosa and Eldridge, no other Redbirds scored in double digits.
Todd McCoy and Gabe Moore each chipped in 10 points for Indiana State.
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