Goals from Damien Duff, Danny Murphy and Andrew Johnson gave Fulham a three-goal lead after the first leg of their Europa League qualifier against NSI Runavik at Craven Cottage.
Duff broke the deadlock when finishing off a sweeping team move with a low shot across keeper Andras Gango.
Bobby Zamora had chances to increase the lead, but was denied by Gango.
Murphy made it 2-0 from the spot after Simon Davies was brought down before Johnson beat Gango from 12 yards.
It was an assured performance from the Premier League side in Martin Jol's first game as manager, although the recently-appointed former Tottenham boss sprang something of a surprise by naming his strongest possible starting line-up.
The Dutchman had hinted he would blood youngsters during the early rounds but instead named a side packed with experience against the minnows from the Faroe Islands.
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.
Duff gave the hosts the lead in the 32nd minute, thumping home from 18 yards after a decent team move from Fulham.
And the Londoners were unlucky to go into half-time only one goal up, with keeper Gango in fine form for the visitors.
The second half proved as one sided as the first, with Zamora dragging a right-footed shot inches wide of the far post early on.
But soon after, Davies was felled by Helgi Lamhauge Petersen when showing nifty footwork inside the box and Murphy slotted the ball into the bottom left of the goal from the penalty spot to make it 2-0.
Johnson then got his name on the scoresheet, firing low across Gango into the corner of the net.
And the score could have been even greater had it not have been for Gango who denied Zamora - who then hit the woodwork - while the keeper later tipped Johnson's strike onto the crossbar.
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.
Fulham manager Martin Jol:
"If I say it is job done , you will tell everyone I said the job was done so I will say it's a good score
"We started off brightly the first five minutes and then it was difficult to find the spare man up front.
"The second half was better. If there was no possibility to play it up to Andy Johnson or Bobby Zamora you have to play down the flanks and the second half was better."