Martin had 19 points, 13 rebounds and three steals for the Buccaneers (10-8, 4-2 Big South Conference), who have won four of their past five and evened the series against the Blue Hose at 7-7.
The Buccaneers led by 15 in the first half and 34-24 at the break.
Presbyterian again got within two points at 70-68 on Khalid Mutakabbir's 3-pointer with 23 seconds left. Charleston Southern hit 6 of 6 foul shots in the final 21 seconds, with Warren sinking four, to seal the win.
Mutakabbir had a career-high 24 points for the Blue Hose.