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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.