Swansea eighth after another Sigurdsson brace
In the day's other league game, bottom club Wigan Athletic were held 1-1 at home by West Bromwich Albion.
Sigurdsson, signed by Swansea on loan in January from German club Hoffenheim, followed up his double against Wigan this month by scoring in the 36th and 66th minutes as Brendan Rodgers's team clinched a third successive victory.
Joe Allen was also on target in the 77th minute at Craven Cottage to lift Swansea to eighth in the table with 39 points from 29 matches. Fulham occupy 11th position on 36.
Sigurdsson glanced in a close-range header to open the scoring after a centre by Wayne Routledge was knocked back across goal by Scott Sinclair.
Swansea went 2-0 up when Sigurdsson side-footed the ball past goalkeeper Mark Schwarzer and Allen made sure of maximum points with a curling right-foot shot following a mistake by Fulham defender Philippe Senderos.
"This was our biggest game of the season purely because it came on the back of last week's win over Manchester City," Rodgers told Sky Sports.
"We don't want our players just to raise their game against the big teams and I thought they were absolutely phenomenal today. It's a very proud day for us all, players, fans and management team."
At Wigan, James McArthur gave the home team a 54th-minute advantage after good work on the wing by Victor Moses.
Wigan, however, were wasteful in front of goal throughout and their former midfielder Paul Scharner headed West Brom's equaliser midway through the second half.
Scharner's goal was the only effort on target all game from West Brom.
"In many ways we feel a sense of footballing injustice because we created chance after chance," said Wigan manager Roberto Martinez. "We could have won by three or four goals, that's how dominant we were.
"Unfortunately there have been too many times this season when our play has not been reflected in the scoreline. That's our big frustration."
Victory would have taken Martinez's team out of the relegation zone and they will look back ruefully on a series of missed scoring opportunites especially by Argentine forward Franco Di Santo.
Emmerson Boyce was also among the Wigan culprits but the best chance fell to substitute Mohamed Diame who missed an open goal when unmarked 10 metres out.