The hosts started off brightly and Chris McCann tried to break the deadlock in the eighth minute by shooting from just outside the area, but Charlton were relatively unharmed after it missed the target.
Charlton had their first shot on goal minutes later but it was safely collected by Burnley keeper Lee Grant.
Despite a positive start, Burnley were dealt a blow when Kieran Trippier was sent off for a handball offence in the penalty area, but the home fans breathed a sigh of relief when shot-stopper Grant managed to save Johnnie Jackson's effort from the penalty spot.
While the home side were able to weather the storm of being down to 10 men in the first half, the second half was a different story as Charlton began to get on top and launch a number of attacking efforts.
Following their goal, Charlton were able to see out the rest of the half and grab maximum points on away turf.