Charlton looked to have sealed a vital point when Darren Bent cancelled out Joleon Lescott's late strike, but a superb volley from substitute James McFadden just seconds from the end ensured his team leapfrog Bolton into fifth place.
Players and fans observed a minute's silence before kick-off to mark the death of Merseyside soldier Adam Smith and the 96 killed in the Hillsborough tragedy.
The game then started quietly with neither side looking menacing in a scrappy, disjointed opening ten minutes.
Then Lescott sped down the left wing and found James Beattie with a crisp cross, but the out-of-form frontman hit a tame volley into the arms of Scott Carson.
But, halfway through the first period, Everton started to turn up the heat at a sun-swept Goodison Park.
First Leon Osman's run and shot was deflected on to the outside of the post before a diving Joseph Yobo came close to connecting with a wickedly curling Mikel Arteta corner.
Soon after, another corner was headed out to midfielder Lee Carsley, who hit a rasping volley that fizzed over Carson's crossbar.
A cleverly worked free-kick saw Arteta feed Osman with a deftly disguised pass, but the midfielder ballooned his shot wide after looking to curl an effort into the top corner.
Charlton offered little and a tame Bent shot was the closest they came to scoring in a one-sided first half.
The Addicks looked a different side in the second half and England hitman Bent should have made Everton pay but he screwed his shot wide when through on goal.
With Charlton bossing the game, Toffees manger David Moyes replaced the hapless Beattie with McFadden.
But it was Charlton who looked more threatening and should have scored through the increasingly lively Bent, before Zhi Zheng missed a sitter.
He volleyed over after which Everton marched up the other end and landed a sucker punch from an Arteta free-kick.
The Basque's pinpoint delivery was met by Andrew Johnson whose parried header fell for Lescott who smashed home.
Charlton though equalised in the last minute as Bent turned the Everton defence inside out before burying his shot in the bottom corner.
But McFadden delivered the killer blow with an exquisite volley from 25 yards out just as Charlton seemed set to grab a share of the spoils.