Vincenzo Montella, Brian McBride and Tomasz Radzinski all got on the scoresheet as the Cottagers eased into the fifth round.
It was a sweet result for club chairman Mohamed Al Fayed who was celebrating his 78th birthday at Craven Cottage.
But it was Montella who was the toast of the Fulham fans after a devastating display that wrecked Stoke's hopes of claiming a major scalp.
On paper this was one of the best Fulham squads for some time after some industrious work by boss Chris Coleman in the January transfer window.
Swollen by the likes of Montella, Clint Dempsey, Simon Davies and now former Chelsea midfielder Alexei Smertin, who watched his new club from the stands after agreeing a move from Dinamo Moscow, Coleman had reason to be happy going into this fixture.
If he was happy before the kick-off then Montella's 10th minute opener added to his delight. The tiny Italian was on hand to bundle home Radzinski's cross for his fourth goal for the club.
Montella's strike brought and end to a sweeping Fulham move. Wayne Routledge started it when his cross was met by Radzinski, whose header was saved by Steve Simonsen. But the Canadian recovered in time to redirect the ball across goal for Montella to stab home.
Stoke's giant team however, were not going to let this match slip without a fight and Ricardo Fuller should really have put them back on level terms in the 20th minute.
The former Portsmouth and Southampton striker climbed virtually unchallenged in the Fulham box but could not direct his header from Dominic Matteo's free-kick past Jan Lastuvka.
But any hopes Stoke had of clawing their way back were dealt a huge blow when McBride doubled Fulham's advantage in the 39th minute.
The American raced on to a wonderful pass from Montella before slotting the ball comfortably under the Simonsen who was rushing off his line to confront the danger.
Stoke squandered another excellent chance to get on the scoresheet when Lee Martin planted his header straight into the hands of Lastuvka in the 50th minute.
And they were left regretting it when Radzinski put the result beyond doubt when he fired home in the 54th minute to make it 3-0.
Montella was again involved when he picked out Moritz Volz with a pass. The German in turn fed Radzinski, allowing the Canadian the simplest of finishes to make it three.
With Stoke looking beaten, Coleman elected to rest Montella in favour of another new signing, Dempsey. The American was soon followed by debutant Davies, who joined Fulham from Everton just three days prior.
And after some switching about, Fulham were again at Stoke and looking to turn the screw as their opponents tired and eventually ran out of puff.
Franck Queudrue floated his free-kick narrowly over late on while Michael Duberry almost turned the ball into his own net right at the death.
Fulham, who last reached the FA Cup final in 1975 when they slumped to defeat against West Ham, were safely through to the next round, while Stoke's supporters were left to travel home licking their wounds.