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.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.