INDIANAPOLIS — Gregg Marshall arrived here in a bit of a cranky mood, accusing the NCAA Tournament committee of scheduling non-Power Five conference entries against one another, the better to get rid of them.

First, the Wichita State coach said mid-major teams have a difficult time getting into the field. Second, he noted that when they are invited, they often play one another in the first round.

“They want to weed out the non-Power Fives as quickly as possible, it appears,” he said on Thursday.

Maybe, maybe not. But the only recourse in such a survival-of-the-fittest world is to win, and so the Shockers did Friday night, 64-58, in a first-round game against fellow non-Power Five power Dayton.

Widely perceived as an unfairly seeded No. 10, the Shockers proved their worth with a gritty, grinding victory that featured 14 lead changes and 11 ties, and in which neither team led by more than five points until about five minutes remained.

When it was over, Dayton coach Archie Miller said Wichita State should have been a No. 4 or 5 seed in its sixth consecutive NCAA appearance.

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The Shockers’ victory set up a rematch with Kentucky of a 2014 game that widely is considered one of the best early-round games in recent NCAA history.

Landry Shamet led the Shockers (31-4) with a mere 13 points. Ten players scored.

As a team, Wichita State totaled 16 turnovers to only six for Dayton (24-8), but it offset that with a 48-29 rebounding edge and a 19-8 advantage in second-chance points.

Scoochie Smith, a senior who grew up in Co-op City in the Bronx, scored 25 points for Dayton, which shot only 31.0 percent from the field — 27.6 percent in the second half.

The Shockers finally broke loose from the tight game when Zach Brown made a three-pointer to put them up 51-45 with 5:40 left. It was 55-51 with 1:27 left when Connor Frankamp made an all-but-clinching three — his only basket of the game. Given Dayton’s poor late-game shooting, it was enough.

“It’s an amazing feeling,” Wichita State forward Markis McDuffie said. “They gave us a 10 seed and a lot of people doubted us.”

Dayton was playing in its fourth consecutive NCAA Tournament and has four senior starters. Said Smith, “It’s just a bad moment, but we did so much in my four years here playing basketball.”

Wichita State is not accustomed to close games, given its dominance of the Missouri Valley Conference. In winning its previous 15 games, it had only one single-digit victory margin. “It was definitely something a little brand-new to us from [what] we’ve seen in the Missouri Valley,” Brown said.

What will it take to beat Kentucky? “It’s going to take a lot,” Brown said.

In closing his postgame news conference, Marshall answered a question that wasn’t asked.

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“I think Dayton deserved a better draw in this tournament,” he said. “I’ll finish with that.”