Arizona, after leading throughout the first half, fell behind by 10 midway through the second period and then staged its own comeback.
Mark Lyons hit a layup for the Wildcats with 22 seconds remaining and was fouled on the play. The ensuing free throw left the game tied at 70-70 and Ohio State then worked the clock down for the final shot.
That shot came from Ross, whose 3-pointer was perfect.
Even though Ross was well behind the 3-point line, the game officials took the time to look at television replays to be sure. That gave Arizona, which did not have a time out remaining, the opportunity to set up a desperation inbounds play.
The length-of-the court pass from Solomon Hill, however, was stolen by Ohio State's Lenzelle Smith to ensure the victory.
Ohio State, which finished a game behind Indiana in the Big Ten Conference regular-season race and then won the league's tournament, will face Wichita State on Saturday for the right to go to the Final Four. The Shockers ended the run of LaSalle in the other regional semifinal contest 72-58.
Deshaun Thomas scored 20 points for the Buckeyes (29-7), who were outshot from the field 44 percent to 42. Ross added 17 points and Aaron Craft had 13.
Arizona (27-8) was led by Lyons with 23 points and Hill with 16.