Carter missed both of his first-half shots but scored the Bobcats' first 10 points of the second half and added another bucket in the 15-4 run that erased Ball State's 37-30 halftime lead.
There were 19 lead changes in the game, the final one coming on Block's straightaway 3-pointer after a shot fake gave him a clear look with 39 seconds left for a 76-74 edge. Two Teyvion Kirk free throws finished the scoring.
Ben Vander Plas grabbed 12 rebounds for Ohio (11-8, 3-4 Mid-American), which swept the season series versus the Cardinals (11-9, 2-5).
Tayler Person scored 21 points to lead Ball State, which made 10 of 18 from the arc but surrendered 23 points off 17 turnovers.
Virginia's Bennett rejects raise in new deal
Virginia coach Tony Bennett turned down a raise while getting an extension, asking that the money be used for the program.
NBA agents reject NCAA's certification proposal
The NBPA sent a letter on behalf of certified player agents to the NCAA that refuses to submit to a proposed certification process to work with undergraduate players testing the NBA draft.
Kentucky gets SF Clarke, No. 4 prospect in 2021
Small forward Terrence Clarke has announced he is headed to Kentucky. Clarke, the No. 4 prospect in the Class of 2021, is expected to reclassify into the Class of 2020.