Branden Dawson added 12 points for the Spartans (5-1), who hung for the win when Elfrid Payton of the Ragin' Cajuns missed a deep 3-point try at the buzzer.
Louisiana-Lafayette charged back from a 10-point deficit with 3:09 remaining, closing to within 62-60 in the final minute, but couldn't get any closer.
Payton ended with 20 points and six rebounds for the Cajuns (2-4).
Shawn Long (16 points) and Kevin Brown (14) also reached double figures in the loss.
Notable deaths of 2014 [PHOTOS]