St. Bonaventure lost its first A-10 home game since February 2017. It had won 14 straight at the Reilly Center in conference play.
Mikesell led the Flyers with 21 points. Crutcher scored 15. Josh Cunningham and Trey Landers each had 14.
Courtney Stockard scored 36 points for the Bonnies (6-12, 2-3), who were playing without two key players, Jalen Poyser and Nelson Kaputo, who average more than 20 points between them.
Dayton returns to action at 7 p.m. Wednesday against George Mason at UD Arena.
Dayton coach speaks after 89-86 win on Jan. 19, 2019, in Olean, N.Y.
St. Bonaventure outscored Dayton Flyers 14-3 in the last four minutes of the first half to take a 34-31 halftime lead.
Dayton led by as many as nine points and had a 28-20 advantage after a 3-point play by Mikesell with 4:42 to play. The Bonnies tied the game on a 3-pointer by Kyle Lofton with 2:02 to play and then ended the half on a 6-0 run.
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Cunningham led Dayton with 11 points. Mikesell added nine. Stockard scored 13 for St. Bonaventure.
Dayton shot 42.9 percent from the field. St. Bonaventure shot 44.8.
There were some tense moments at the end of the half as both teams converged on the court with both coaches trying to separate players.