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.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.