Smith took a pass from Tarry Rozier and knocked down a jumper from the left wing with 0.3 seconds to play to steal the win for the Cardinals (23-4, 12-2 ACC), whose winning streak was extended to 10 games.
Montrezl Harrell led Louisville with 21 points. Rozier scored 11 off the bench.
Sean Kilpatrick led Cincinnati (24-4, 13-2) with 28 points, but was the only Bearcat in double figures. He also sank five consecutive free throws at the end of the game to give Cincy a 56-55 lead with 1:40 to play.
Cincinnati shot just 28.6 percent from the field compared to 40 percent for Louisville. The Cardinals went 3-for-11 from 3-point range and converted only 11 of their 22 free throws.