Brian McBride scored the only goal in a scrappy match that failed to get going until the hour.
The visitors had the better of the opening exchanges as they went in search of the first win at Craven Cottage since 2001. The industrious Phil Neville added bite to their midfield and allowed Tim Cahill to make his trademark surging runs.
It was on one of these forays that he won the ball and poked the ball through to Mikel Arteta on the edge of the box. The Spaniard ran into the box before unleashing a powerful shot that fizzed past the far post with Tony Warner watching.
Cahill again was involved just a minute later, spreading the ball wide to an equally advanced Kevin Kilbane to swing the ball in. Marcus Bent made a desperate run to get on the end of the cross, but the ball sailed just over his head.
As Everton surged Fulham continued to ride their luck at the back. Both Zat Knight and Carlos Bocanegra were guilty of being caught in possession of the ball when they should have cleared their lines and Fulham were lucky not to be punished early on.
The visitors relied on soaking up the Everton pressure and counter-attacking with some success. McBride hit an early effort over the bar and Luis Boa Morte's intelligent run saw him meet McBride's cross at the near post, but the captain slid the ball wide from six yards out.
An angry exchange between the Fulham captain and Nigel Martyn ensued as the keeper was annoyed that Fulham continued to attack whilst two Everton attackers lay on the floor with injuries sustained in the previous assault on the Fulham goal. A quiet word from referee Mike Riley was enough to diffuse the situation.
Everton's grip on the game continued to tighten as the game went on and Bent was again guilty of missing the target with a header when Tony Hibbert swung in a useful ball to the striker.
Warner almost handed the opener to Bent when he sliced his clearance into the air and then completely missed the ball when trying to head the ball clear.
Coleman's half-time talks must be the stuff of legend as Fulham emerged a different side and took a surprise lead in the 62 minute through McBride.
Steed Malbranque sent Moritz Voltz into the box with a delicate pass and the German full-back cut the ball back intelligently for McBride to sweep the ball home from the penalty spot.
The home side almost doubled their lead just minutes later when Malbranque's mishit cross almost sneaked in and drew a good save from Martyn.
Everton tried to hit back and almost drew level at the last through substitute Duncan Ferguson but the Scot's powerful header from close range was palmed away by Warner.
As they became increasingly desperate tempers began to flair as the tackles went in. Neville saw red after picking up his second yellow card of the game for a late tackle on Tomasz Radzinski.
The visitors may count themselves unlucky to come away from this game with nothing, but it is welcome relief for Fulham boss Coleman.