Trist made 14 of 18 shots from the floor for the Leopards (1-1), who connected on 53.1 percent of their shots (34 of 64) to the Blackbirds' 40.9 percent (27 of 66).
Trist, a sophomore forward, made the first two baskets of overtime and Lafayette never surrendered the lead. The Blackbirds (0-2) got within a point, 95-94, with 2:03 left before a free throw by Tony Johnson and two by Seth Hinrichs put it away.
Hinrichs had 20 points and Johnson 16 for the Leopards.
Jamal Olasewere led LIU Brooklyn with 25 points and 11 rebounds, and Jason Brickman and C.J. Garner added 19 each. Garner's layup with 18 seconds left in regulation sent the game into overtime after a second half with 12 lead changes.