The Cottagers finally overcame the Northern Ireland Premier League side in the first leg of their second qualifying round tie with late second-half strikes from Bobby Zamora and Danny Murphy after the Belfast team had cancelled out Matthew Briggs' opener through Timmy Adamson.
It was a hard-fought victory for Martin Jol's men on the sapping 4G artificial surface at Seaview in Belfast.
It took the London side 10 minutes to carve out their first opportunity when Damien Duff cut in from the right and shot straight at keeper Sean O'Neill.
That was the first of three good chances for the Republic of Ireland international in the first period.
On the other flank, Swiss youngster Karim Frei also impressed, cutting in from the left wing and testing O'Neill on two occasions.
From set-pieces, Brede Hangeland was making a nuisance of himself and twice almost converted far-post headers.
After 39 minutes, Crusaders squandered a series of chances to clear Danny Murphy's corner, with the ball eventually rolling out to young full-back Briggs, who rifled it back into the top-left corner of the net to open his account for the club.
Any hopes Fulham had of a straightforward second half soon evaporated as the home team came out at a rasping tempo, Adamson dragging wide after a neat turn two minutes after the restart.
The striker made no mistake seven minutes later when he brought down the ball on the edge of the six-yard box, beat the advancing Aaron Hughes and flicked the ball past Mark Schwarzer's outstretched hand.
Seaview erupted and minutes later it almost got even better for the home support when Adamson crashed a close-range shot off the crossbar.
But just as the whiff of upset was in the air, Fulham snuffed it out, regaining the lead with 15 minutes left when Zamora rose at the near post to head home a Duff corner.
Two minutes later, Crusaders' brave resistance was ended when defender Paul Leeman handled an Andrew Johnson shot in the area to concede a clearcut penalty.
Murphy converted in clinical fashion, sidefooting the ball low to O'Neill's left.
The second leg takes place at Craven Cottage next Thursday.