The Addicks extended their unbeaten run to five matches with another fine team display.
The Toffees had previously only been beaten once in nine away matches and that was against Premiership leaders Chelsea so this was a notable scalp for Charlton.
The first half was a real cat and mouse affair with very few opportunities as neither side were prepared to give any ground.
In the rare forays on goal Charlton's Jonathan Fortune poked the ball wide from a free-kick and Shaun Bartlett headed over while Everton's best opportunity came from a well-struck Marcus Bent shot which was turned away for a corner by Dean Kiely.
A minute before the break Everton lost their keeper Nigel Martyn with a pulled muscle and he was replaced by Richard Wright.
The second half was a much more open affair with Bartlett and Jerome Thomas both going close for Charlton while at the other end Hermann Hreidarsson scrambled a Thomas Gravesen corner off his own line.
The deadlock was finally broken eight minutes from time when Danny Murphy's corner found substitute Paul Konchesky who crossed the ball back into the goalmouth for Moroccan international Talal El Karkouri to head the ball into the net.
A minute later there was more bad news for Everton when Duncan Ferguson, who had only been on the field for eight minutes after coming on as a substitute for Bent, was sent off by Mike Riley for elbowing Hreidarsson in the face.
Charlton increased their lead five minutes from time when another Murphy corner caused confusion in the Everton defence and Hreidarsson was able to volley the ball home at the far post.
Everton have already surpassed all expectations this season by reaching 40 points on Boxing Day, a point more than they achieved in the whole of last term but they met their match at The Valley.