Smith slightly rushed his attempt, but it gave the team its third title in school history. The shot put Republic (27-4) ahead for the first time since the Tigers held a 6-5 lead with 7:06 left in the second quarter.
Smith finished with 14 points. Dylan Bekemeier and Cody Geiger both added 13.
Xavier Kurth led Lafayette (25-5) with 13 points. The Fighting Irish used a 12-2 second quarter run to take a 17-8 lead with 57 seconds remaining in the first half and led until the 1:01 mark of the fourth quarter before Geiger tied the score at 42 with two free throws.
Smith's shot was the only scoring the rest of the way.