Blackburn scored three goals in the last 15 minutes to pull off an amazing win and reach the quarter-finals.
Charlton seemed to be cruising after Danny Murphy set up Darren Ambrose for the opener and hit the second himself.
Substitute Shefki Kuqi gave Rovers hope by scoring less than two minutes after coming on before fellow replacement David Thompson equalised from 30 yards.
David Bentley then hit a dramatic winner to put Rovers through and seal Charlton's fifth successive defeat.
The recalled Murphy set up Charlton's first chance by putting Alexei Smertin through, but his shot deflected off Andy Todd for the game's first corner.
Jonatan Johansson was then thwarted by Rovers keeper Brad Friedel after a good flick by Darren Bent.
At the other end Dean Kiely, in his first game of the season after injury, made a good save from Craig Bellamy in a one-on-one.
Bellamy's bad luck continued as he had an effort ruled out after the referee decided that Morten Gamst Pedersen's cross had gone out of play as it flew into the Charlton penalty area.
As the half wore on, Charlton looked the more dangerous side and Bent and Smertin both came close within a minute of each other.
Murphy was becoming increasingly influential and it was no surprise that he was involved when Charlton took the lead with the best move of the half.
He played the ball on to Johansson and he laid it into the path of Ambrose who drilled it past the helpless Friedel.
The goal sparked Rovers into life and Bellamy missed a great chance to equalise as he got in-between Kiely and Hermann Hreidarsson but the ball ricocheted off him and over the bar.
Charlton started the second half with a flourish and Ambrose produced some superb skill, switching the ball from left to right foot, before being denied by Friedel.
And less than a minute later Murphy doubled the lead as Blackburn dallied on the edge of their own area and he nipped in to pinch the ball and fire it into the net.
Rovers were doing little and Charlton fans were beginning to think the game was all over but suddenly Kuqi gave the visitors a lifeline.
He forced his way past Talal El Karkouri and toe-poked the ball past Kiely less than two minutes after coming on.
Suddenly Rovers sensed a chance and they quickly equalised when Thompson dispossed Radostin Kishishev and rocketed a superb 30-yard shot into the net.
And the comeback was complete when Bentley fired home Pedersen's pass to seal an amazing victory and earn a place in Saturday's draw.
Charlton manager Alan Curbishley
"You just can't defend like that and it seems as if one or two of them are on a death wish.
"I don't think you can make the last 15 minutes up and we have destroyed a fantastic opportunity in this cup.
"I can't allow this to keep happening. We've gone from ecstasy to despair in four weeks and must now regroup and get out there on Sunday to get this club a result - because we certainly need it."
Blackburn manager Mark Hughes
"At 2-0 you think you are going out of the competition but I shouldn't have doubted the players as I know their qualities and determination.
"Once we got one goal there was always a likelihood we would get back on level terms - and then of course there was always the possibility of a winner.
"Thankfully the substitutions got us back into the game and we are delighted with the performance in the end."
Charlton: Kiely, Young (Spector 70), El Karkouri, Hreidarsson, Powell (Bothroyd 89), Johansson (Hughes 79), Kishishev, Murphy, Smertin, Ambrose, Bent. Subs Not Used: Myhre, Thomas.
Goals: Ambrose 37, Murphy 50.
Blackburn: Friedel, Khizanishvili, Nelsen, Todd, Gray, Emerton (Kuqi 73), Savage (Thompson 63), Reid, Pedersen, Bentley (Mokoena 90), Bellamy. Subs Not Used: Enckelman, Matteo.
Booked: Reid, Bellamy, Bentley.
Goals: Kuqi 75, Thompson 81, Bentley 88.
Ref: P Walton (Northamptonshire).