An early goal and a miskicked clearance from Edwin Van der Sar gave Everton three points as new boss Davis Moyes looked on.
Fulham were caught cold in the very first minute of the match after David Unsworth fired the home side in front.
Everton were then grateful recipients of a terrible error from Dutch 'keeper Van der Sar as he horribly scuffed a clearance into the path of Ferguson to double Everton's lead.
With Gravesen receiving his second yellow card in the first half, Jean Tigana made a double substitution at half time as Fulham looked to take full advantage of the extra man.
Despite coming close with Louis Saha again hitting the bar, Fulham could only score the one goal courtesy of Steed Malbranque.
Nonetheless, the second half was especially nervy for Moyes as Fulham piled on the pressure. The Toffee's new boss was glad to hear the final whistle and praised the White's passing game.
"It was hard, and we couldn't get out of our own half. When you're down to 10 men there are few teams who can pass the ball as well as Fulham do. They are a good side."
The defeat leaves the Whites sitting in 12th position; five points above third from bottom Bolton Wanderers.
Speaking after the match, Jean Tigana remained claim and insisted that his side will not revert to a long ball game in order to keep away from a relegation dogfight.
"We need to change our ways but we need to keep playing, that is my philosophy and I don't want to change. In football at the highest level you have to keep playing. Even if we are in a position where we are relegated I will keep this philosophy.
"I thought we started the game 10 minutes too late. That was our problem, and when you concede two goals it's very difficult to come back.
"I understand that we lost but it is not acceptable for me to ask my team to kick opponents because I have respect."
However, talk of falling into a relegation battle was somewhat premature for Tigana as he reaffirmed his dedication to playing passing football.
"It's better for me, it's good for the crowd and it's good for the younger players. If you want to play at a high level you have to play like this. The next game against Tottenham is a big game, we have to forget about today and try to win."