Anthony Drmic scored all 11 of his points in the second half and the Broncos have started 3-0 for the third consecutive season. Elfrid Payton and Alan-Michael Thompson scored 12 points apiece for Louisiana-Lafayette (1-2).
Boise State used a 9-0 run over a nearly seven-minute stretch of the second half to take control.
The Broncos trailed 52-50 with 7:50 remaining after a basket by Louisiana-Lafayette's Bryant Mbamalu. Drmic hit a go-ahead 3-pointer 26 seconds later to start the decisive run as the Ragin' Cajuns didn't score again until Thompson's basket with 55 seconds left.
Boise State jumped out to a 20-6 lead less than 11 minutes into the game before the Ragin' Cajuns rolled off 19 straight points over a seven-minute span to take a five-point lead. Louisiana-Lafayette led 28-26 at halftime.