The West Londoners are many people's relegation favourites but new boss Coleman sent his side out to prove everybody wrong.
The first goal came after just ten minutes when Carlos Marinelli won the ball from Martin Djetou before stroking the ball past the Fulham keeper.
It was a disastrous start for the home side but they hit back seven minutes later. Jerome Bonnissel delivered a deep cross which Louis Saha managed to flick on, and Marlet arrived at the far post to volley the ball past Mark Schwarzer.
Fulham continued to dominate but had to wait until the second half to extend their lead.
Junichi Inamoto produced a contender for miss of the season as he miskicked from six yards on 54 minutes, but he made amends two minutes later as he hammered home a fierce shot to complete a fantastic Fulham move.
Ten minutes later Inamoto turned villain as he handled in his penalty area. However, goalkeeper van der Sar spared his blushes by producing a great full stretch save from Malcolm Christie.
Saha added a third for Fulham on 69 minutes as he volleyed home from ten yards out.
Substitute Szilard Nemeth offered Boro a lifeline when he beat van der Sar to the ball 30 yards out and looped the ball round the keeper and into the net.
Boro boss Steve McClaren said: "It must have been a great game for a neutral as both teams went for it. Unfortunately I think the defining moment was the penalty, but it was a great game of football.
"But if we keep playing like that I think we'll win more than we'll lose. We don't normally concede three goals away but we learnt a lot about ourselves today.
"Fulham boss Coleman was delighted and said: "We've had a bit of a dodgy press recently and I think we were more up for it because of that.
"I was more than pleased with the way our team played and took the game to Middlesbrough in the end."