The Seagulls had to play 83 minutes with 10 men following the seventh-minute sending off of defender Inigo Calderon.
The Spaniard was shown a straight red card following a crunching tackle on Therry Racon.
Top scorer Johnnie Jackson gave Charlton the lead in the third minute with his 10th goal of the season from the penalty spot after Marcos Painter was penalised for a foul on Joe Anyinsah.
Brighton hit back to equalise nine minutes before the interval through striker Glenn Murray, who expertly hooked in a ball from defender Adam El-Abd.
Charlton striker Paul Benson wasted a chance to give his side victory in the last minute of normal time by shooting tamely at Danish keeper Casper Ankergren.
Charlton keeper Rob Elliot came to his side's rescue in stoppage time by saving well from former Addicks midfielder Radostin Kishishev.
Brighton 1-1 Charlton: Match Report - view commentary, squad, and statictics of the game as it happened.