Ahearn, the country's top free throw shooter for the past three years, was 14-of-14 from the line against the Shockers.
Missouri State (12-3, 3-1 Missouri Valley Conference) led by as many as 19 several times in the second half -- the first after Wichita State coach Mark Turgeon received a technical foul for arguing a foul call against one of his players.
With the Bears leading 76-57 midway through the second half, Wichita State (10-5, 1-3) went on an 8-0 run and cut the lead to 76-65 with 7:54 left.
The Shockers pulled to within seven at 88-81 with 1:16 left in the game, but a Wichita State turnover after stealing the inbounds pass led to an uncontested Missouri State basket and a nine-point lead with 1:03 remaining.
The two teams exchanged free throws the rest of the game.
Devin Mitchell had 19 for Missouri State.