Adonis De La Rosa scored 13 of his 17 points on free throws for the Golden Flashes (17-16), who will play top-seeded Buffalo in Friday's first semifinal. The Bulls advanced with an 89-74 win over Central Michigan.
Walker was the tourney's MVP last year when the Golden Flashes knocked off the top three seeds.
With the Golden Flashes clinging to a one-point lead, Avery darted through traffic and scored to make it 74-71. Ball State's Tahjai Teague missed a 3-pointer and Walker dropped a free throw to put Kent State up four.
Tayler Persons, who scored 19 points, hit a runner to pull the Cardinals within 75-73 before Kent State guard Kevin Zabo split a pair of free throws, giving Ball State one last chance.
However, the Cardinals (19-13) couldn't get a clean look as the horn sounded.
Avery and Kevin Zabo scored 16 apiece for the Flashes, who split their two games with Buffalo during the regular season.
Teague added 17 and 12 rebounds for Ball State.
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