The Buckeyes won their third in a row and find themselves in fourth place in the Big Ten Conference race, 1 1/2 games behind front running Indiana. Ohio State will visit the Hoosiers on Saturday.
Northwestern, which suffered its sixth straight loss, took a one-point lead with 4:06 to play when Reggie Hearn made a 3-pointer.
Smith's 3-point shot came 15 seconds later and started a 15-4 surge to finish the contest. Smith led the Buckeyes (21-7, 11-5 Big Ten) with 24 points and Deshaun Thomas added 19. Ohio State committed only six turnovers and forced 15.
Northwestern (13-16, 4-12) was paced by 14 points off the bench by Tre Demps.