Dickson Etuhu fired newly-managerless Rovers into an early lead but Johnnie Jackson made amends for missing a penalty when he struck Charlton's equaliser.
The draw came barely 24 hours after Kean, having travelled down to London with the Rovers squad, suddenly decided to quit.
After months of constant speculation about his job and protests against him from supporters, the Scot had finally come to the conclusion his position was "untenable".
Former Ewood favourites Alan Shearer and Tim Sherwood are being linked with the role, with the latter's club Tottenham understood to have already been approached by Rovers.
But whether either would fancy working with controversial owners Venky's remains to be seen.
In the meantime Eric Black, Kean's assistant, took charge for the clash at The Valley.
The Rovers fans who had made the trip seemed strangely subdued at kick-off, perhaps still nursing hangovers from last night's celebrations sparked by the news Kean had walked.
But they woke up with 16 minutes on the clock when the recalled Morten Gamst Pederson played in Etuhu, who danced between the static Chris Solly and Michael Morrison before rifling the ball into the net.
'Stand up, if you're glad he's gone', came the chant from behind the opposite goal.
It was poor defending from Charlton, though, after they had almost gone ahead themselves a minute earlier when Salim Kerkar's low drive fizzed narrowly wide.
And the hosts should have drawn level in the 26th minute when Pedersen was adjudged to have brought down Leon Cort in the area.
But Jackson's penalty, blasted straight down the middle, was kept out by the legs of the diving Paul Robinson.
It was only a brief let-off for the visitors, however, as 60 seconds later Jackson diverted a shot from Danny Green past Robinson.
With Blackburn now penned in their own half, Green took aim again from the edge of the area but this time his effort was deflected onto a post.
After the break Robinson made a point-blank save to keep out Cort's header, Bradley Wright-Phillips nodded another dangerous Kerkar cross over and Green's drive was inches too high.
At the other end Nuno Gomes volleyed over and Jordan Rhodes headed wide.
In stoppage time Robinson tipped over an acrobatic scissor-kick from Wright-Phillips to secure Rovers' point, while their fans will feel they scored a more important victory last night.
