Exeter thought they had taken the lead in the 14th minute after Addicks keeper Ben Hamer parried Rowan Vines' initial effort into the path of Daniel Nardiello, whose follow up shot looked to have crossed the line.
But the officials were unconvinced and play continued, much to the fury of Nardiello, who refused to let the matter drop and was shown a straight red card five minutes later for dissent after continuing to protest to the linesman.
Charlton struggled to make their numerical advantage count but they finally made the breakthrough two minutes before the break when Bradley Wright-Phillips and Paul Hayes exchanged passes before Wright-Phillips fired past Exeter keeper Lenny Pidgeley.
The Addicks had to wait until the 81st minute to finally make the game safe and this time Wright-Phillips turned provider by delivering a low cross from the right which was fired home by Dale Stephens.
Scott Wagstaff almost added a third moments later when he met a Rhoys Wiggins cross, but his shot was saved by Pidgeley.