Terel Hall's basket gave Savannah State the lead at 31-25 with 16:19 left but the Tigers wouldn't make their next field goal until Khiry White hit a shot with 1:39 remaining. They made 12 free throws during the stretch.
Florida A&M went on an 8-0 run to take a 46-43 lead with 5:14 left. Neither team would score again until Jamie Adams' free throw at the 2:13 mark.
Savannah State would get within one-point on two occasions in the final minute.
Jamari Bradshaw added 11 points for Florida A&M (8-14, 4-5 Mid-Eastern Athletic Conference). The Rattlers held a 54-39 advantage on the glass.
Hall scored 11 for Savannah State (8-15, 6-3), while Jyles Smith added 10 and 12 rebounds.