Mortimer shot 7 of 10 from the field and a perfect 3 of 3 from behind the arc while Eaves hit 8 of 11 free throws.
Tashombe Riley added 12 points and seven rebounds for the Bulldogs (4-4, 1-0 MEAC), who shot 53.8 percent from the field.
A K'Ja Johnson 3-pointer gave Florida A&M a 29-21 lead, its largest of the first half, with 5:27 left. But South Carolina State closed on an 11-6 stretch to trim the lead to 35-32 at the break.
The Bulldogs momentum continued into the second half, as they finally took and kept the lead for good on a Gabriel McCray 3-pointer with 8:37 remaining.
Francois Lewis led the Rattlers (3-6, 0-1) with 18 points.