Eagles' goal was no less than Blackpool had deserved, as they were comfortably the better team during the early stages.
Eagles almost restored Blackpool's lead before the interval, but drilled over from 20 yards.
The Addicks improved in the second half, playing with a quicker tempo and noticeably more ambition and they took the lead for the first time 10 minutes after the restart.
With Morgan Fox making a smart decoy run down the left, Cousins was able to drive forward with the ball in space and curl it into the bottom corner.
As both sides pressed for the game's fourth goal, McMahon was lucky to escape without a caution following an elbow to Cousins' face on 65 minutes.
Kevin Foley nearly grabbed an equaliser as the game entered its final stages, but his shot was blocked by his own man on the line.
Davies eventually turned his effort home following a scramble in the box, salvaging the point for the Championship's bottom club.
Charlton's Andre Bikey did have a chance to steal a winner deep into stoppage time, but fired over with the goal gaping.