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.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.