The Blackbirds (9-10, 4-3 Northeast Conference) made 18 of 24 shots in the second half, when they came back from a 33-21 deficit to defeat the Terriers (8-10, 4-3) for the fifth straight time.
Garner scored 17 second-half points, including 10 during a 22-6 run that gave LIU Brooklyn a 62-50 advantage with 4:36 remaining.
Jalen Cannon had 21 points and 10 rebounds for St. Francis.
The series between the two schools, situated slightly over a mile apart, has been billed as the "Battle of Brooklyn" since the 1975-76 season.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.