The Addicks took the Seagulls to penalties as the match finished 0-0, winning 4-3 in the shootout.
Advertisement
While their World Cup winner Alexis Mac Allister was partying in Buenos Aires, and has been given two weeks off, his teammates headed to The Valley with a place in the last-eight up for grabs.
Roberto de Zerbi fielded a strong line-up that featured the likes of Moises Caicedo, Adam Lallana, Tariq Lamptey and Lewis Dunk.
Advertisement
A farcical shoot-out began with Pascal Gross, Jayden Stockley and Leandro Trossard all hitting the woodwork.
Brighton keeper Jason Steele looked set to be the hero, saving from George Dobson and Jes Rak-Sakyi.
But when March ballooned his effort over and Maynard-Brewer saved from Caicedo, Sam Lavelle stepped up to send the Addicks, who are 18th in League One, through.
De Zerbi said: "I'm sorry for the result and sorry for our fans, we wanted to win the game and play in the quarter-finals.
Advertisement
Advertisement
"I think we played a good game, not a fantastic game but enough to win the game.
"We made a lot of mistakes in the last five metres. We had opportunities to score. And in penalties you can lose. We had match point with March but we made another mistake and when you make another mistake you have to lose."
Advertisement
It is the first time Charlton have made the quarter-finals since 2006.
The Addicks join Leicester, Newcastle, Southampton, Wolves, Nottingham Forest, and Manchester United in the next round.