Chris Hughton's team had surrendered pole position to Middlesbrough after their promotion rivals won at Ipswich on Friday and it seemed they would squander the chance to regain first place when they fell two goals behind in the opening five minutes at the Amex Stadium.
Teenager Ademola Lookman slammed home his first senior goal for struggling Charlton in the second minute and Reza Ghoochannejhad added a second three minutes later.
But Manchester United loanee James Wilson pulled one back for Brighton in the 50th minute and the Seagulls turned it around after Charlton defender Patrick Bauer had been sent off for a foul on Bobby Zamora.
Former Tottenham forward Zamora levelled in the 83rd minute and substitute Tomer Hemed headed an 85th-minute winner to put Brighton two points clear of Middlesbrough.
Fourth placed Hull lost ground on the top two after they lost 2-1 at Leeds.
Chris Wood gave Leeds a 30th-minute lead and Tom Adeyemi doubled their advantage 15 minutes later.
Ahmed Elmohamady's header got one back for Hull six minutes after the restart but the hosts held on.
Will Keane came out on top in a family affair at Turf Moor as Preston won 2-0 against his twin brother Michael's Burnley.
Preston striker Keane, closely marked by centre-half Michael, struck the opening goal in the 63rd minute and Daniel Johnson added a second in the closing stages.
Huddersfield registered their first win in three attempts under head coach David Wagner as their first away success since September, 2-0 at Birmingham, lifted them out of the relegation zone.
Joe Lolley struck after just 31 seconds and Nahki Wells' close-range finish ensured a first win in seven for the Terriers.
Bottom of the table Bolton slumped to their ninth defeat of the season as Cardiff won 3-2 at the Macron Stadium.
Gary Madine cancelled out Tony Watts' 13th-minute opener for the Bluebirds before Bolton hit the crossbar through Darren Pratley's 44th-minute effort.
Cardiff regained the lead through Scott Malone in the 53rd minute and although Dorian Dervite equalised, Anthony Pilkington lashed home an 80th-minute winner.
Brentford made it four games unbeaten with a 2-0 home win against Milton Keynes Dons in Dean Smith's first game in charge.
Two Matt Mills headers helped Nottingham Forest secure a 3-0 victory against Fulham at the City Ground.
Bristol City had defender Nathan Baker sent off in a 2-0 home defeat against Blackburn, while Wolves won 2-1 at second bottom Rotherham.