The Bulldogs (17-9, 9-5 Horizon League) won their third straight despite playing without center and leading scorer Matt Howard, who sat out with a mild concussion he suffered against Illinois-Chicago on Monday.
After Zach Hahn's 3-pointer with 2 minutes remaining in the first half, Butler never trailed.
Wright State got within 64-60 and had the ball with 50 seconds remaining, but Evans' missed jumper was its last gasp. With the Raiders forced to foul, the Bulldogs made 7 of 8 from the free throw line down the stretch.
Butler starting guard Chase Stigall, who suffered a leg injury against UIC, started on Thursday and did not score. He went 0 for 6 from the floor.