Indiana led 63-59 with a minute to go, but Branham hit a pair of free throws to cut the lead in half then set up E.J. Liddell’s game-tying dunk with six seconds left.
In overtime, he tied the game at 67 with a driving layup then found Jamari Wheeler wide open for a 3-pointer that gave the Buckeyes a 70-67 lead they would not relinquish.
Liddell finished with 16 points and seven rebounds while Eugene Brown III added 10 for Ohio State.
Xavier Johnson led Indiana with 16 points while Trayce Jackson-Davis and Race Thompson added 13 apiece.
The Hoosiers (16-10, 7-9 Big Ten) remained winless in February and missed a chance to pick up an NCAA Tournament resume-booster.
Ohio State (17-7) bounced back from a deflating loss to Iowa on Saturday, the Buckeyes’ first at home this season.
They remained a game back in the loss column in the Big Ten standings, improving to 10-5 in the league while Purdue is 13-4 and Illinois and Wisconsin are both 12-4.
Ohio State led 50-39 early in the second half before the Hoosiers surged in front with a 20-5 to set up the final stretch.
The win got a busy week off to a good start for the Buckeyes, who play at Illinois on Thursday night and at Maryland on Sunday afternoon.
They also have three games next week as they continue making up games postponed because of COVID-19 regulations earlier in the season.
Nebraska comes to VCA on March 1 with Michigan State visiting two days later and the regular season concluding at home against Michigan on March 6.
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