The game was just five minutes old when Vratislav Gresko was skinned by Steed Malbranque, who had the freedom of the Rovers half to manoeuvre.
His low ball across the six-yard line should have been cut out by both Brad Friedel and Martin Taylor and Luis Boa Morte could not believe his luck when the ball arrived for a tap-in.
Rovers rarely threatened in a dismal first half, Fulham's tactics of containing Blackburn with a five-man midfield working to perfection.
After the break, the home side showed a little more urgency but were undone by a classic sucker-punch.
The woeful Gresko again gave away the ball, it was hoofed over the top to Louis Saha who exposed Lorenzo Amoruso's lack of speed before burying his shot beyond Friedel.
With the game played in a flat atmosphere in front of just 21,985 supporters, Blackburn needed someone to lift the team.
That man could have been Brett Emerton, but Edwin Van der Sar pushed away his stinging drive.
Fulham should have had a penalty when Lee Clark was felled by Nils-Eric Johansson and Andy Cole was unfortunate to hit the crossbar after a great piece of skill enabled him to lob Van der Sar, but as Souness later admitted, it was Fulham's day.
Blackburn: Friedel, Martin Taylor, Amoruso, Babbel, Gresko, Emerton, Ferguson, Flitcroft, Thompson, Cole, Jansen. Subs: Tugay, Johansson, Grabbi, Yorke, Kelly.
Fulham: Van der Sar, Volz, Goma, Knight, Bonnissel, Pembridge, Inamoto, Boa Morte, Clark, Malbranque, Saha. Subs: Melville, Djetou, Leacock, Buari, Crossley.
Referee: M Messias (N Yorkshire)
Attendance: 21,985