Carlton Cole scored two Barclays Premier League goals in a single game for the first time in his career as West Ham United recorded a first away win in 28 top-flight matches.
The England striker pounced in each half at a chilly Craven Cottage either side of a Frederic Piquionne volley. Aaron Hughes had earlier put the home side in front with a free header.
The three points - which owed much to the magnificent Robert Green in goal - moved the Hammers off the bottom and level on 16 points with their opponents. The last away win came at Wolverhampton Wanderers on the first day of last season - 15 August 2009.
Avram Grant had made five changes to his starting lineup, although the back four were unchanged in front of Green, who had recovered after missing the 1-1 draw at Blackburn Rovers last week following minor surgery.
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Freddie Sears, back from loan, and Junior Stanislas occupied the wide positions, with Radoslav Kovac in alongside Scott Parker in midfield with Fulham old boy Luis Boa Morte suspended. In truth, Fulham dominated the first half once Hughes had headed in unmarked on ten minutes.
For all their possession play, Fulham could not find a second past Green and paid the price when Dickson Etuhu diverted the ball into Cole's path. The No9 slid in and fired in under Mark Schwarzer.
That was nine minutes before the interval and the Hammers looked like heading into half-time on level terms. Piquionne had other ideas, though, and found space at the back post to smash Parker's delightful cross beyond Schwarzer in added time.
After the restart, the Hammers were imperious and - with Matthew Upson and James Tomkins standing firm - marched on to a memorable away win. Cole sealed the deal when he found room in the penalty area and shot into the far corner beyond Schwarzer.
Both teams had their moments after that but the away side were always on top. Sears and Stanislas both had good chances in the closing stages but none of the travelling support minded too much that the chances went astray. Grant and his men will be on a high for Everton on at home on Tuesday.