The frustrating stalemate against the Faroe Islands part-timers in the first qualifying round second-leg clash at the Svangasgard Stadium meant the Cottagers won 3-0 on aggregate.
Martin Jol's side will now head to Belfast next Thursday to face Steven Baxter's Hatchetmen.
Damien Duff hit the crossbar after five minutes and then sliced a shot over from six yards out as Fulham peppered the NSI goal but they could not find a breakthrough.
It was the hosts who created the only clear-cut chance of the second half when Klaemint Olsen shot wide from inside the box.
While most Premier League clubs have only just returned to pre-season training, Fulham were in competitive action for the second time. The first leg was played on June 30.
The 2010 runners-up qualified via the Fair Play league and still have 21 matches to negotiate if they are to reach the Europa final again.
Belfast will be Fulham's next port of call and their progress was never in doubt following their 3-0 first leg win at Craven Cottage.
Jol made four changes but was still able to send out another strong starting line-up.
Defenders Aaron Hughes and Chris Baird, the only two squad members to have played in the Faroe Islands before, did not travel and were replaced by Stephen Kelly and Philippe Senderos.
Jonathan Greening took over from Simon Davies on the left flank and Steve Sidwell replaced Danny Murphy in central midfield and Fulham were in control from the outset.
Bobby Zamora headed an early chance over the top before Duff, one of the first leg goal-scorers, struck the bar from 25 yards with a left-foot drive after cutting in from the right wing.
Fulham kept that early pressure up for the remainder of the half but could not find a breakthrough, with Gango denying Andrew Johnson on three occasions.
Duff sliced a shot over the bar from just six yards out and Matthew Briggs was also off target with a close-range header as Fulham struggled to make their ascendancy count. NSI were well organised.
Left-back Jens Joensen was booked eight minutes before the interval for checking Johnson. Dickson Etuhu met Greening's free-kick but his header was straight at Gango.
Sidwell was booked early in the second half for a hard challenge on Mamuka Toronjadze, despite appearing to win the ball.
Duff and Briggs both tried their luck from distance with no luck before Jol began to make changes, with Kerim Frei and Bjorn Helge Riise sent on for Johnson and Greening.
Fulham, struggling to create any clear cut chances, then survived a scare when Olsen burst into the box and sliced his shot wide of Mark Schwarzer's left-hand post.