Martin scored 15 points and grabbed 10 rebounds for the Buccaneers (3-2), who also got 14 points from Arlon Harper.
Stetson led 26-22 at the break, but Jeremy Sexton pulled Charleston Southern even at 32-all with a 3-pointer less than five minutes into the second half.
The teams kept trading leads, with Joel Naburgs hitting a 3 to put Stetson back ahead 51-49 with 7:25 left. But Muo answered with a 3-pointer of his own, starting an 11-0 run for the Buccaneers.
They wouldn't trail again, outscoring the Hatters 51-38 in the second half to seal the comeback win.
Both teams grabbed 34 rebounds each, but Charleston Southern forced 26 turnovers.
Aaron Graham led the Hatters (3-2) with 17 points.