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Ryan Mikesell led the Flyers with 19 points. Obi Toppin scored 18, adding another strong performance to his resume but falling short of 20 for the first time this season. Ibi Watson added 16. Crutcher had 12.
Dayton (5-1) heads home on Thursday night and returns to action Tuesday against Houston Baptist.
Halftime recap: The Flyers made their first five 3-pointers, withstood a run by Kansas and built a 37-36 halftime lead.
Dayton made 8 of 18 3-pointers (60 percent) in the half. Ibi Watson made 3 of 6 and led the Flyers with 11 points.
Toppin was held scoreless for most of the half but got going late and scored seven.
» HISTORIC OPPORTUNITY: Dayton seeks rare top-five win
Devon Dotson scored 17 points for Kansas. The Jayhawks trailed 17-14 and then went on a 10-2 run.
Dayton, which did not score in the last two minutes after taking a 37-33 lead, led by as many as four points. Kansas led by as many as five. It was an intense, back-and-forth first half.
Each team had five turnovers. Kansas outscored Dayton 8-3 at the free-throw line.