The victory ensures Albion move back to the top-of-the-table and equal Queens Park Rangers record of 19 games unbeaten in the Championship in one season.
For 80 minutes it looked as though Albion would slip to a first defeat as Chartlon raced into a two-goal thanks to strikes from Ademola Lookman and Reza Ghoochannejhad inside five minutes.
But Albion were handed a lifeline on 50 minutes as James Wilson, in his first Bighton start, embarked on a fine solo before firing past Henderson to pull one back.
Patrick Bauer was then shown a straight red for pulling back Bobby Zamora with 31 minutes left, before Zamora and Tomer Homed struck in the final ten minutes to complete a remarkable turnaround.
Charlton found themselves ahead after just two minutes following a quick breakaway goal.
Reza Ghoochannejhad lead the counter before slotting Ademola Lookman in, with the wideman firing a left-foot strike from a tight angle past David Stockdale.
It got better for The Addicks just three minutes later as they added a second. Another quick break was led by Lookman and he found Johann Gudmundsson who crossed for Ghoochannejhad to add a second.
Ghoochannejhad so nearly had a second on 19 minutes as he headed Ricardo Vaz Te’s header towards goal only to see his effort parried behind for a corner by Stockdale.
Charlton were continuing to look dangerous and Albion once again had Stockdale to thank for keeping it at two 11 minutes later.
Lewis Dunk gave the ball away and Vaz Te went racing away down the right and crossed for Gudmundsson but his shot was superbly stopped by Stockdale.
Solly March came close to pulling one back on 32 minutes after making room for a left-foot strike, though, his effort went just over.
Albion were gifted a chance five minutes before the break as Stephen Henderson fumbled Jamie Murphy’s cross to Dale Stephens but his shot from 18-yards sailed well over.
Charlton could well have made it three in first-half injury-time they broke through Ghoochannejhad and he fed Lookman who jinked in on his right only to see his shot well saved by Stockdale once again.
The Seagulls made a fine start to the second and pulled one back on 50 minutes. James Wilson, who was making his first Brighton start, waltzed through and fired under Henderson.
March thought he had levelled the scores three minutes later with a 25-yard thunderbolt but, with Henderson beaten, his effort struck a post.
Charlton were then reduced to ten-men with 31 minutes left as Patrick Bauer hauled down Bobby Zamora on the edge of the area and was consequently shown a straight red.
Beram Kayal so nearly netted from the consequent free-kick, though, it struck a Charlton boot and sailed behind for a corner.
Albion pressed hard in the closing stages and their efforts were rewarded in an amazing final ten minutes.
First, Zamora was on hand to level things up with six minutes left with as he fired home from six-yards.
Then, less than a minute later, substitute van La Parra’s perfect cross was met by Hemed to complete a remarkable trunaround.
BRIGHTON: Stockdale; Bruno, Greer, Dunk, Calderon; March, Stephens, Kayal, Murphy; Zamora; Wilson. Subs: Maenpaa, Huenemeier, Hemed (Murphy 72), Manu, Ince, van La Parra (Calderon 82), Chicksen (Wilson 93).