Tobias Linderoth's first ever goal for Everton sunk Charlton in this scrappy Carling Cup third round tie at a rain-soaked Goodison Park.
The match started at a frantic pace with both sides creating good early chances.
In the fifth minute Thomas Gravesen whipped a cross in which Toffees striker Duncan Ferguson met with a powerful header directed straight into the arms of Addicks keeper Dean Kiely.
The irrepressible Wayne Rooney latched onto a loose ball on the halfway line on nine minutes, ran at the Charlton defence, and chipped an audacious lob over the bar from 25 yards out.
Charlton though were playing the better football and created the best chances through Jason Euell. The striker should have broken the deadlock after 39 minutes when he brilliantly controlled a Radostin Kishishev long ball but he shot against the legs of Nigel Martyn from five yards out.
And, just three minutes later, Everton took the lead. A deflected volley from Rooney cannoned back off the bar leaving Lindroth free to head into an empty net.
Euell was again guilty of wasting a gilt-edged chance on 53 minutes, side-footing a Jonatan Johansson cross horribly wide with the goal gaping.
Everton pressed for a second with the young Scotland international James McFadden terrorising the Charlton defence and on 63 minutes Tony Hibbert centred a low driven cross which Gravesen hit first time from 20 yards, only to see Kiely tip it over the bar.
Charlton fought hard for an equaliser and Hermann Hreidarsson stabbed a shot agonisingly wide of the right hand post as they pressed deep into the four minutes of added time to set David Moyes' nerves jangling.
But the Toffees' defence stood firm as they eased into the fourth round.