A sellout crowd of 12,012 showed up to watch the first on-campus game between the in-state schools since 1921.
Jackson scored 13 points while teammate Kaleb Wesson had 15 to lead the Buckeyes.
Kyle Young had 10 points and eight rebounds for Ohio State while freshman guard Lutehr Muhammad added 11 points.
Wilmington native Jarron Cumberland scored 22 points -- all in the second half -- to lead the Bearcats.
After both teams struggled to find the range in the first half, Ohio State made 11 of 20 (55 percent) from the field in the second 20 minutes while the Bearcats were 13 for 33 (39.4 percent).
Ohio State leads Cincinnati 27-18 at the half in the season-opener for both teams.
The Buckeyes led by as many as 10 late in the first half thanks to a C.J. Jackson 3-pointer with 1:29 left.
That capped an 8-3 Ohio State run.
Kyle Young led the Buckeyes with six points while Jackson added five.
The Buckeyes shot just 33.3 percent from the floor (9 for 27) but held the Bearcats to 13.8 percent (4 for 29).
Cincinnati had twice as many fouls (eight) as field goals in the first half, though Ohio State also had more fouls (11) than field goals.
Wilmington native Jarron Cumberland, expected to be UC’s leading scorer this season after the Bearcats lost three of their top threats from a year ago, played only four minutes in the first half because of foul trouble. He was scoreless.
Ohio State and Cincinnati are set to do something rare: Play a basketball against each other.
The Bearcats are re-opening Fifth Third Arena, and the Buckeyes are the guests for the first regular season game.
Here’s a look around the building.
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The teams last played a game against each other on one of the team’s campuses in 1921. They last played at UC in 1920.