Yoann Barbet marked his return to the side with the equaliser after Brentford had fallen behind inside 19 seconds.
Charlton, who have won only once since mid-November, went in front straight from the kick-off.
Morgan Fox scampered up the left flank and aimed a cross at Yaya Sanogo, and although the Arsenal loanee couldn’t make anything of it, the ball fell for Callum Harriott to crash home.
Brentford struggled to find any rhythm in the first 20 minutes, not helped by a series of niggly fouls by Charlton’s midfield.
John Swift headed the first chance wide when unmarked and Alan Judge, cutting in from the left, saw his attempt for the far corner clawed away by Charlton keeper Nick Pope.
As Griffin Park stood and applauded after 24 minutes, in memory of supporter Dean Langford who died aged 24 last week, the Bees found a burst of inspiration to equalise.
Marco Djuricin was denied by Pope in a one-on-one but from the following corner, Barbet nodded in as the perfect tribute.
Sanogo could have restored Charlton’s lead but put Harriott’s cross wide.
Brentford: Button; Yennaris, Dean, Barbet, Bidwell; McEachran, Woods; Canos, Judge, Swift; Djuricin.
Subs: Bonham, McCormack, O’Connell, Kerschbaumer, Saunders, Hofmann, Vibe.
Charlton: Pope; Motta, Fanni, Teixeira, Fox; Gudmundsson, Cousins, Diarra, Yun; Harriott, Sanogo.
Subs: Mitov, Johnson, Bergdich, Ghoochannejhad, Poyet, Lookman, Makienok.