Ian Chiles added 15 points for the third-seeded Bears (15-13), who will face seventh-seeded Coppin State on Friday. Cedric Blossom chipped in 12 points and Anthony Hubbard cleared 11 boards.
Jamie Adams scored 26 points while Jomari Bradshaw finished with 12 for the sixth-seeded Rattlers (14-18).
Morgan State shot 36.1 percent from the field in the first period and led 31-29 at the break. Florida A&M made 40 percent of its field goal tries, but attempted six fewer shot attempts.
The Bears came out of the half on fire, as they drained 57.7 percent of their field goal tries in the second frame. Morgan State was up two points with 17:49 left when it went on a 14-0 run to bust the game open.
Morgan State dominated the glass, as it outrebounded the Rattlers 48-31.