Ron Baker went 12-of-14 from the foul line en route to 15 points for the Shockers (13-0), who completed a perfect non-conference schedule and extended the best start in school history.
Fred VanVleet delivered the knockout blow on a 3-pointer with 3:48 remaining for a 71-64 Wichita State lead.
Darius Carter helped out with 13 points and Tekele Cotton added 10 with four blocked shots.
Davidson (4-9) got 17 points, six assists and six rebounds from Tyler Kalinoski.
Celebrity Couples of 2014 [PHOTOS]