Jon Stead scored his first goal for Sheffield United to help his side move seven points clear of the drop-zone.
Stead celebrates after scoring his first goal for United
Stead opened the scoring when he forced his way through the Fulham defence before firing into the roof of the net.
The Blades made it 2-0 when Michael Tonge converted Stephen Quinn's cross and Rob Hulse almost added a third when he smashed a late shot against the bar.
Fulham had not lost for 10 games but were second-best throughout and did not even force a save from Paddy Kenny.
The win was United's first at Bramall Lane in 2007 and eases their relegation fears, although they remain in 16th place in the Premiership.
Fulham's impressive run has seen them climb away from danger themselves in recent weeks - but they were brought crashing back down to earth here.
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The visitors got a taste of what was to come when the Blades launched their first attack in the opening minute.
Hulse fired over from Colin Kazim-Richards' low cross and Cottagers keeper Antti Niemi got a whack in the teeth for his trouble as he dived at the striker's feet.
Niemi, playing his first game since injuring his neck against Watford on New Year's Day, needed lengthy treatment but showed no ill-effects when he turned Quinn's low shot around the post soon afterwards.
But the home side were already well on top and it was no surprise when they took the lead on 23 minutes.
Stead was first to Montgomery's driven cross and before the Fulham defence could react he had steadied himself and lashed the ball into the roof of the net.
This was only the 23-year-old's third appearance for United after a £750,000 move from Sunderland earlier this month - and he has already matched his tally from the whole of last season in the top-flight with the Black Cats.
Warnock's side were not finished yet however.
Quinn chased a loose ball in the box and sent in another cross that Ian Pearce tried to clear - but he could only direct the ball against Tonge and the ball rolled into the net.
Fulham could not muster an attack of note in response before the break and did not improve much after half-time either.
Stead and Hulse's ability to hold up the ball continued to bring Tonge and Montgomery into the game from central midfield - and Quinn and Kazim-Richards were a constant threat on either flank too.
In contrast Fulham, who lost Vincenzo Montella to injury early on, made little impact in the final third and were reduced to thumping the ball forward by the end.
If the visitors had run out of ideas then the Blades were full of them.
Hulse twice almost got on the scoresheet himself late on when he saw a near-post header saved by Niemi then hit the bar after a mistake by Pearce.
And a third goal would not have flattered the home side, who were comfortable winners by the end.
Sheffield United manager Neil Warnock:
"The manner of the win was excellent. We scored two goals and we created a lot more chances.
"When we had to defend we coped well and I don't think Paddy Kenny had a shot to save - it was a thoroughly professional performance.
"I was delighted with every member of the team. I really enjoyed the game because we dominated for long periods."
Fulham boss Chris Coleman:
"From start to finish we were very disappointing. We did not force their keeper into a save and did not deserve anything from the game.
"I've come to expect a certain level of performance from this team and I did not see this coming."
"We have let ourselves down and our fans down. It is a long way to come on a cold night and we did not perform."
Sheff Utd: Kenny, Geary, Jagielka, Lucketti, Armstrong, Kazim-Richards, Tonge, Montgomery, Stephen Quinn, Hulse, Stead.
Subs Not Used: Bromby, Webber, Alan Quinn, Fathi, Nade.
Goals: Stead 23, Tonge 28.
Fulham: Niemi, Rosenior, Knight, Pearce, Queudrue, Davies, Volz (Dempsey 82), Brown, Radzinski (Routledge 74), Montella (Helguson 33), McBride.
Subs Not Used: Lastuvka, Omozusi.
Ref: L Mason (Lancashire).