Savannah State (4-1) outscored Clemson 17-3 at the start of the second half to cut a 22-point halftime deficit to 44-36 with 14:40 remaining. But Clemson finished with a 31-9 run to put the game away.
Clemson, which is off to a 6-0 start for the fourth straight season under coach Oliver Purnell, blocked 14 shots and outrebounded Savannah State 47-28.
Anthony Jones scored 20 points for Savannah State, but no other visiting player managed to score more than six.
Raymond Sykes added 14 points and seven rebounds for Clemson.
Clemson scored nine of the game's first 11 points en route to a 41-19 halftime lead.