Defender Chris Baird struck twice early in the first half to help Fulham move out of the relegation zone and ease the pressure on manager Mark Hughes.
Baird opened the scoring after only four minutes when his vicious 20-yard strike flew in off the post.
And he doubled the lead with another fierce drive from the edge of the area, this time low into the right corner.
Stoke pressed gamely but clear chances were few and Fulham held on to record a first away league win in 16 months.
In this rollercoaster of a Premier League season it appears that statistics and form count for very little.
The Cottagers had previously gone eight games without a win and had slipped into the relegation zone over Christmas, with boss Hughes criticised by fans after their 3-1 home defeat by fellow basement battlers West Ham on Boxing Day.
However, despite their wretched record of not having won a top-flight away game in their last 26 attempts, Fulham showed no signs of travel sickness against Stoke.
As if spurred on by the recent barbs and an increasingly perilous league position, Hughes's side raced out of the traps, starting the game as though Premier League survival depended on the result of this encounter.
With last season's star striker Bobby Zamora out of action because of a broken leg, the London side have found goals hard to come by in recent weeks.
Hughes salutes 'huge' Fulham display
But, rather than make a change up front, Hughes shuffled his defence for this match, replacing Carlos Salcido with Baird, in a move which few would have predicted would prove decisive.
The first half was only four minutes old when Simon Davies's cross was headed away from danger by Robert Huth, only for Baird to take the ball in his stride and rifle his right-footed effort towards the corner from the edge of the box.
The home side's goalkeeper Asmir Begovic managed to palm the drive on to the post but the sheer pace of the shot forced the ball into the net.
And it was the trusty right foot of Baird which did the damage again six minutes later.
Pulis blames defeat on 'flat start'
This time the defender was teed up by Andrew Johnson's short free-kick on the edge of the box and Baird hammered his low drive beyond Begovic's outstretched left arm and into the bottom corner, doubling his goal tally for the season and stunning the home crowd.
Stoke boss Tony Pulis had seen his side comfortably beat Fulham 2-0 in the Carling Cup in September but the Potters were clearly rattled by the visitors' high-tempo start.
And it was not until Ryan Shawcross's towering header was cleared off the line by Danny Murphy on the stroke of half-time that Stoke started to crank up the pressure and suggest they were capable of getting back into the match.
Predictably in the second half it was the Potters, who went searching for goals as Fulham sat back to defend their lead.
And the home fans were incensed as two penalty claims - both for handball - were turned down.
Baird delighted with double strike
Firstly, Jones headed on to the arm of Johnson in the box but, with the former Everton striker knowing little about it, the referee waved play on.
Secondly, Breda Hangeland dived in front of Matthew Etherington's drive but the referee appeared to signal the ball had struck Hangeland's chest - with replays proving inconclusive.
Stoke threw men forward in numbers as they attempted to find a way back into the game, and Mark Schwarzer was forced into a low save from Huth's close-range effort.
But the Cottagers showed a resolve which will doubtless delight Hughes as his side go into the second half of a season requiring more afternoons like this one before their top-flight status is assured.
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