Cannon finished with 26 points and 15 rebounds and moved into first place on the school's career-scoring list with 1,667.
Jones had three assists, moving him into sixth on the NEC career assist list.
Two free throws by Fall started a 7-0 run which gave St. Francis a 71-66 lead with 58 seconds left in overtime.
Gerrell Martin converted a three-point play to pull LIU Brooklyn (12-16, 8-9) within two, but Fall and Jones combined to go 3 of 6 from the stripe, and the Blackbirds went scoreless, from there.
Martin and Nura Zanna scored 12 apiece for LIU Brooklyn.