The Cougars were clinging to a 77-76 lead with under a minute to go when Gibson grabbed an offensive rebound and dunked to put Houston up by three with 49 seconds left.
Florida A&M's Jamie Adams missed a 3-pointer, Thomas added one of his five blocks and J.J. Thompson sank two free throws after a steal to seal the win. Jherrod Stiggers added 19 points for the Cougars and Gibson also had 10 rebounds.
Florida A&M led by one at the half and scored the first five points of the second half to go up 40-34. Instead, the Cougars climbed back into it behind Gibson and Thomas.
Adams and Reggie Lewis led the Rattlers with 18 points each.