The top-seeded Tar Heels played their first game all season without star guard Kendall Marshall, who sat on the bench with a broken wrist bone. His absence showed as North Carolina turned the ball over 23 times and faced the prospect of becoming an upset victim.
The Bobcats inched in front by four in the game's final 7 minutes and they still led by one before North Carolina's Reggie Bullock hit a 3-pointer with 42 seconds left in regulation.
Walter Offutt then tied it with 25 seconds, making a layup while being fouled by Stilman White. Offutt missed a free throw that would have put Ohio in front and the game went to overtime when Offutt blocked a jump shot by Harrison Barnes with 4 seconds left.
North Carolina (31-5) dominated the extra period, getting a 3-pointer from Bullock and jumper from Barnes to take a 68-63 lead.
The Tar Heels will face Kansas Sunday in the regional final after the Jayhawks survived an upset bid of their own in downing North Carolina State.
Tyler Zeller hit 8-of-14 shots and scored 20 points for North Carolina. Bullock scored 17, with five of his six field goals coming from 3-point range.
Offutt hit six 3-point shots and scored 26 for the Bobcats (29-7), who reached the NCAA tourney by winning the Mid-American Tournament as the No. 3 seed. Ohio was seeded 13th in the Midwest Region, but stunned Michigan in the second round.