After the hosts spurned a number of openings after the visitors had taken the lead, Manuel Pellegrini's men punished their hosts with two clinical finishes, as West Ham eased to a comfortable win after the break to leave to Cottagers rock bottom of the Premier League table.
The Hammers' fourth win on the bounce sees the visitors record their best top-flight run since 2013.
Hammers pounce on nervy hosts
On a drenched evening in west London, both sides struggled to get to grips with the conditions as the ball slithered around on the Craven Cottage surface in a scrappy opening spell of the game.
With the hosts visibly nervous propping up the league table as they were at kick-off, it took Andre Schurrle's shy from distance to wake the Cottagers from their early lethargy.
Soon after, Aboubakar Kamara was then denied by Lukasz Fabianski one-on-one, after Aleksandar Mitrovic's clever through ball sent the Frenchman in on goal only to be denied by the Polish stopper.
Seconds later, Fulham were punished as the Hammers hit first. After a mis-timed tackle by defender Denis Odoi, Felipe Anderson flipped the ball over the defender and slid a ball centrally to Snodgrass. The Scot received the ball and coolly hit a first-time left foot effort curling past Sergio Rico and into the net to open the scoring.
Having lost their chance for a first clean sheet of he season after less than 20 minutes, the hosts again looked uncertain on the ball. They responded well however and then failed to level with three chances in as many minutes.
The so far quiet Mitrovic found space on the edge of the area, and running in with an angled diving header, could only nod down and wide of near post. Kamara was again handed another two openings with a header from Odoi's cross, and then moments later with an effort from the edge of the box, both of which were comfortably saved by Fabianski.
Fulham piled forward, but just as their season had gone thus far, Claudio Ranieri's men were caught cold on the counter-attack. Again Anderson was architect-in-chief as the Brazilian's whipped cross reached Javier Hernandez whose knock-down fell to Antonio to poke home from close range.
With a mountain to climb, Schurrle and skipper Tom Cairney also bent further efforts wide and over the bar from 20 yards out before half-time, after what was a clinical first-half display from West Ham.
Stubborn defence frustrates Cottagers
Fulham began the second period with urgency and with substitute Cyrus Christie introduced on the right, the west London side were finding greater space on the wing.
Indeed it was Christie's driven cross across the West Ham boughs that hit Issa Diop before being scrambled away by the Irons' back line.
It was not only the French centre-back that was a towering figure in West Ham colours. Mexican Fabian Balbuena was again a rock at the back for Manuel Pellegrini's men, throwing his body in the way of almost all that moved toward the danger area, as Fulham searched to claw their way back into proceedings.
With Mitrovic an increasingly isolated figure up front, the Cottagers began to look short of ideas with few sources of creativity, as West Ham began to set-up to catch out the hosts and pile further pressure on the home goal with the pace of Anderson on the break.
Hammers cruise to win
In truth however, the two goals had blown the early winds of optimism from the Fulham sails, as the hosts ran a rather toothless second period race.
Anderson did however notch a late goal from close range but was denied but a firm stop by Rico, as Ranieri watched on with much to ponder ahead of the festive schedule.
The win for West Ham sees the east Londoners win their fourth game on the bounce and climb into the top half of the league standings, as the hosts contemplate what could be an uncomfortable Christmas in west London.