Sims made four 3-pointers for the Eagles (12-13, 5-6 Mid-American), who shot 63 percent from the floor in the second half.
Jauwan Scaife led the Cardinals (10-14, 4-8) with 21 points but was just 6 of 18 from the floor, including 2 of 13 from 3-point range. Conference rebounding leader Majok Majok grabbed 16 rebounds and scored six points.
Eastern Michigan won despite getting outrebounded 33-23 and committing 15 turnovers. Ball State's shooting woes helped: The Cardinals shot just 34 percent and made just six of their 20 shots after halftime. They were 5 of 27 from 3-point range for the game.
With the win, Eastern Michigan avenged Jan. 9's 60-58 home loss to Ball State. The Cardinals still lead the all-time series, 54-39.
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Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.