In an incredible end to the game, Blackburn came from two goals down to snatch a 90th minute equaliser from their goalkeeper Brad Friedel, who had come up for a corner but sensationally deep into injury time.
Charlton snatched a dramatic winner with a brilliant 25-yard volley from Danish international sub Claus Jensen to shatter Rovers, who dominated the game for long periods, especially in the second half.
The win moved Charlton back into fifth place, but they gave a very nervy display after looking as though they were coasting to a comfortable victory at the interval.
Before the match, Curbishley had challenged his players to stand up and be counted and halt their worst run of form for a year following the departure of their star player Scott Parker to Chelsea.
His players certainly responded in the early stages of the game, although they were very subdued despite taking a tenth minute lead through on-loan striker Carlton Cole.
With his back to goal he was allowed to turn unchallenged by two Rovers defenders and fire a rocket shot into the net after being played in by Paolo Di Canio.
But it was Blackburn who then took control of the game, Brett Emerton saw his shot tipped over the bar by Dean Kiely and recent signing Jon Stead, who scored on his recent debut following his move from Huddersfield, hit the post for the visitors.
Against the run of the play, Charlton increased their lead with a scrappy goal which was again poorly defended by Rovers.
A long ball was headed on by Di Canio and Jason Euell dropped behind the visitors' defence to stab the ball home at the second attempt.
Stead then fired over the bar with another good chance, but the youngster did not reappear after the break because of a hamstring injury and Andy Cole, who replaced him, made a significant difference as Blackburn battled their way back into the game.
They reduced the arrears when they were gifted a goal after Cole intercepted a dreadful backpass from Radostin Kishishev. Even then, Cole took an eternity to put the ball into the empty net, but the goal saw Charlton's confidence visibly drain away from them as they tried to hang on to the points.
But in the last minute, Blackburn goalie Friedel left his goal unguarded at one end to race the length of the field as Blackburn got a last ditch corner.
The ball was driven in hard and low by Paul Gallagher and Kishishev's clearance rebounded off the visitors' goalkeeper into the net and seemed to have given the Lancashire side a deserved share of the points.
But the drama was still to come as Charlton were awarded a free-kick, which was taken by their skipper Matt Holland. Hermann Hreidarsson headed the ball into the path on Jensen, who crashed a 25-yard thunderbolt into the top corner of the net despite the frantic attempts of the luckless Friedel to keep it out.
Although he got his hands to the ball, the power of the shot was too much for him as he agonizingly watched it nestle in the corner and Charlton celebrated their good fortune.
Charlton: Kiely, Kishishev, Perry, Fish (Fortune 15), Hreidarsson, Young, Holland, Euell, Stuart, Di Canio (Konchesky 89), Cole (Jensen 77).
Subs Not Used: Royce, Johansson.
Blackburn: Friedel, Babbel, Short, Todd (Yorke 59), Gray, Neill, Flitcroft (Tugay 28), Emerton, Douglas, Gallagher, Stead (Cole 45).
Subs Not Used: Enckelman, Andresen.
Attendance: 26,332
Referee: U Rennie (S Yorkshire)