The Explorers (7-3) trailed 39-33 with 3:03 left until halftime before scoring six straight. La Salle's Jerrell Williams tied the game at 39-39 on a layup with 1:05 left until halftime.
Darryl Shazier put the Bison (4-7) back ahead 41-39 on a layup with 2 seconds remaining in the first half.
La Salle opened the second half on a 9-2 run and led 48-43 on Williams' layup with 15:16 left to play.
Williams scored 14 points and Aaric Murray added 12 for the Explorers.
Murray was 3 of 3 from 3-point range as La Salle, ranked No. 12 in 3-point percentage (42.5), shot 46.2 percent from long range (6 of 13) against the Bison.