Marcus Posley added 12 points off the bench for the Cardinals (4-4), and Chris Bond had 11 points and 11 rebounds. Majok, a junior-college transfer coming off a career-high 17 rebounds in Wednesday's win over Holy Cross, grabbed 16 boards and added nine points.
Steve Tecker had 15 points and Trevor Gruis 14 for the Coyotes (4-6), who tied the back-and-forth game at 39 on Brandon Bos' 3-pointer with 12 minutes to play. But a 15-5 Ball State run, capped by Scaife's 3-pointer with 5:53 left, put the Cardinals up 54-44. South Dakota later pulled within 54-51 but didn't score again.
Ball State shot 43 percent from the field, but that was better than South Dakota's 34 percent -- including 4 of 25 on 3-pointers.