Buoyed by back-to-back wins over Wigan and title-chasing Manchester City, the visitors secured another three points in west London to propel them up to eighth.
Swansea looked dominant throughout at Craven Cottage, with Sigurdsson scoring a goal in each half.
The on-loan Hoffenheim midfielder broke the deadlock with a first-half header and set the Swans on course for victory in the 66th minute with his fourth goal in three games.
Fulham came into the match unbeaten in six home games in all competitions, but looked second best throughout and Joe Allen wrapped up a convincing victory in the 77th minute.
Clint Dempsey came closest for the Cottagers with a late shot that hit the bar, although Swansea held out to record a 12th clean sheet.
Mahamadou Diarra was handed his first Fulham start for today's game, while Bryan Ruiz was also drafted in.
Danny Murphy and Damien Duff dropped to the bench as a result, while Swansea made one enforced change to the starting line-up.
Ashley Williams saw his run of 169 consecutive appearances brought to an end by a virus and was replaced in central defence by Garry Monk.
The match was built up as one between two sides that play with an attack-minded philosophy and neither needed any encouragement to go forward.
Having seen Danny Graham force goalkeeper Mark Schwarzer into action after just 30 seconds, Fulham were soon testing Swansea stopper Michel Vorm.
First the Holland international expertly tipped over a goalbound Dempsey effort, before Moussa Dembele opened his body up to force Vorm into a low save.
Neither side, though, were managing to stamp their authority on the opening exchanges as chances came at both ends.
Scott Sinclair saw an effort blocked after an uncharacteristic mistake by captain Brede Hangeland, before left-back John Arne Riise fired over from the edge of the box as Fulham ventured forward.
There was a real sense of frustration by the Thames as both teams struggled to play their normal games, epitomised by a wayward Dempsey drive that was followed by a shrug of the shoulders.
Swansea, though, were managing to show flashes of their exquisite passing game, which almost resulted in a 29th-minute opener when Sigurdsson saw a low effort creep inches wide.
Ruiz tested Vorm with an audacious long-range effort when the hosts returned to the attack, although their defence was looking unusually haphazard.
Schwarzer was one of the guilty parties and, after seeing a clearance charged down, had to be on his toes to thwart Sinclair.
However, Fulham did not take heed of the warnings and found themselves a goal behind in the 36th minute.
Wayne Routledge darted down the right flank and sent a cross to the back post, which was head back across goal by Sinclair for Sigurdsson to nod home.
Dembele had an effort blocked as Fulham looked for an immediate response, although that was as close as they came as the first half came to a close.
Chants of 'Come on Fulham' rang out around Craven Cottage at the start of the second period as the home faithful tried to spur their side on.
The Whites, though, were struggling to find a way past Swansea's resolute defence, leading boss Martin Jol to replace the ineffectual Ruiz with Duff after 54 minutes.
The Ireland international brought a new attacking intent to the right flank and blazed over almost immediately, before then seeing a shot blocked.
But it was Swansea that looked in control and few could argue when they doubled their advantage in the 66th minute.
Sigurdsson was again the scorer as he slotted past Schwarzer after outfoxing the Fulham defence with a neat one-two with Routledge.
Fulham brought on Kerim Frei and Murphy as a last throw of the dice, but it could not stem the Swansea tide.
The Cottagers were made to pay for a misplaced Philippe Senderos pass in the 77th minute as the ball was worked to Allen, who went past the Switzerland international to fire home.
The home support left in their droves after Swansea's third, although the only moment of note they missed was a Dempsey shot that Vorm tipped on to the bar.