Midway through the first-half the game sprang into life when McCarthy tested Schwarzer with a fierce drive from 20-yards which the Fulham keeper palmed away for a corner.
From the resulting kick, which McCarthy miss-hit, Duff on the near post knew little as the ball rebounded off him and into the direction of Samba who stabbed the ball past Schwarzer.
Allardyce pleased to see off Fulham
To their credit Fulham responded brightly with Dempsey crashing a stunning overhead kick against the bar before testing Robinson with a low effort from 12-yards after losing his marker with a turn Johann Cruyff would have been proud of.
Duff also forced a decent low save from Robinson with a swerving shot, while at the other end Martin Olsson tested Schwarzer with his 18-yard strike.
Blackburn increased their lead after the break and it was again McCarthy who was the provider, with the South Africa striker whipping in a fine free-kick, which an unmarked Taylor headed past Schwarzer at the near post.
Fulham's afternoon got worse when Dempsey was forced off with a knee injury - the American was later sent to hospital for a scan - while defender Paul Konchesky also went off with an ankle injury.
Hodgson wants Fulham to regain 'edge'
Even so the visitors were soon back on the attack and Robinson, who was having a fine afternoon, did well to save Zoltan Gera's half-volley from the edge of the area, which he saw late as it came through a crowd of players.
Fulham claimed a penalty when substitute Erik Nevland was pulled back by Samba as he raced through on goal but their appeals came to nothing as Blackburn held out for a victory that lifted them into 12th place.
The Cottagers have now not won in the Premier League since beating Manchester United just under a month ago, though Roy Hodgson's side remain eighth.
Blackburn boss Sam Allardyce: "It has been a difficult period and it's nice to get a win after the run we've had. We've been drawing too many games.
"We got the first goal and for the first time in a long time we've got the rub of the green.
"It was a good time to score after half time and it is a big, big win. It is well deserved and one that will take the pressure of us.
"We had a good solid defensive unit today and the keeper pulled off a couple of saves when we needed.
"The performance was nice but it was all about the result today and we're pleased to get the victory."
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