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.
We have changes at the top of the draft and a shakeup in the lottery, with teams starting to make their final decisions. Get the latest in Chad Ford's mock draft.
Duke freshman point guard Derryck Thornton Jr. is transferring to USC, his father announced on Friday to Scout.com.
NBA draft prospect Kris Dunn is excited to see Game 7 between the Cavaliers and the Warriors, he breaks down the constant comparison between LeBron James and Steph Curry and looks forward to playing with or against some of these guys next season.