Smith's heroics enabled the Buckeyes (12-0) to reel off 14 points in the final minute, overcoming a 58-50 deficit to remain undefeated.
Smith's three foul shots with 32.9 seconds left pulled the Buckeyes to within 60-59, and Ohio State went ahead 16 seconds later after Smith converted a layup on a pass from Aaron Craft.
Craft then made a defensive stop at the other end on Notre Dame's Jerian Grant and Smith followed with two free throws with 9.8 seconds left.
Grant made 1-of-2 free throws with 6.7 seconds to go and a Craft drained a foul shot to make it 64-61 with 3.3 seconds left.
Demetrius Jackson missed a 3-point try as time expired for the Fighting Irish.
LaQuinton Ross provided 16 points and 11 rebounds for Ohio State.
Grant led Notre Dame (8-4) with 18 points.