Damien Duff, Danny Murphy and Andrew Johnson netted the all-important goals in their first round first-leg qualifier at Craven Cottage as the west Londoners look to repeat their run to the final in 2010.
While a further 22 matches still stand between them and another appearance in the finale, Fulham already seem to have dispatched NSI with a clinical display in the first leg of their first qualifying round clash.
Heading into the tie, recently-appointed boss Martin Jol sprang something of a surprise by naming the strongest possible starting line-up.
The Dutchman had hinted he would blood in youngsters during the early rounds but named a side packed with experience.
Murphy skippered the Whites and the likes of Brede Hangeland, Bobby Zamora and Duff were included in the starting line-up.
The home side started strongly and within the opening minute Johnson came close to breaking the deadlock, but Helgi Petersen blocked well after neat build-up play by Murphy and Zamora.
The Cottagers continued to dominate the opening exchanges, although they struggled to get out of second gear and past NSI's backline.
Zamora attempted a neat header on the quarter-hour mark as Fulham looked to break the deadlock, while Johnson's pace continued to threaten the Faroese side's defence.
Duff was unfortunate not to net the game's first goal in the 23rd minute, twisting and turning on the edge of the box before unleashing a right-footed drive that went just wide of the far post.
Despite Fulham's dominance, Justinus Hansen almost gave NSI a shock lead with a thumping effort that caught Mark Schwarzer unawares and bounced just wide.
The long-range drive seemed to spur Jol's side into life and - after some nice play down the left-hand side - Duff thumped home from inside the 18-yard box.
The Republic of Ireland international's 33rd-minute goal did not open the floodgates, although NSI goalkeeper Andras Gango was forced to tip over smartly from a curling free-kick from Zamora on the stroke of half-time.
Fulham returned from the break reinvigorated and the visitors were forced to deal with a barrage of attacks from the offset.
Gango palmed away efforts from Johnson, Hangeland and Zamora shortly after the restart, before the latter and Duff blazed wide.
Despite NSI's resilience, however, the home support did not have to wait long for a second goal after Petersen upended Simon Davies in the box, allowing skipper Murphy to coolly slot home from the penalty spot.
Gango was called into action again moments later, with Johnson forcing the Hungary-born goalkeeper into a fine save.
However, the NSI goalkeeper could do nothing about the Cottagers' third goal as Johnson wriggled free in the box and angled a shot into the bottom left-hand corner.
The 30-year-old saw another effort hit the bar shortly after, before Jol rang the changes in a bid to freshen his side up - handing a debut to former Liverpool man Lauri Dalla Valle.
Murphy attempted a speculative effort in a last bid to get the 14,910 fans on their feet again but Fulham were restricted to a three-goal advantage heading into next week's second leg.