After a bright start from the Canaries, Fulham's right-wing combination of Sascha Riether and Pajtim Kasami forged an opportunity on 16 minutes, with the latter delivering a low ball to Darren Bent who blasted in the opening goal.
The goal brought a needed composure to Fulham in midfield and they went on to take control. Ashkan Dejagah grabbed the second on 41 minutes with a solid finish from close range with Girogos Karagounis and Alex Kacaniklic the architects.
Chris Hughton's substitutions had a tame effect on the game and midway through the second half and the excellent workhorse Steve Sidwell powered home his third goal in successive matches after a deep cross from Riether.
Rene Meulensteen's side will make the trip to Brammall Lane on Sunday January 26 to face the Blades who defeated Aston Villa last week, while the odds will shorten on Hughton to be next Premier League manager to lose his job after an eight successive defeat.
2' - CHANCE NORWICH - Great start for the away side. Redmond coming close, initially, before Robert Snodgrass smashes the crossbar from 25 yards out.
16' - GOAL FULHAM - The opener for Fulham with a super combination on the right-wing. Sascha Riether works with Kasami, his cross dummied smartly by Dejagah for Darren Bent who makes no mistake from close range.
41' - GOAL FULHAM - Second goal for the Cottagers; Karagounis carves open the Norwich defence with a through ball to Kacaniklic, the Swede cutting back for the Iranian international Dejagah to slam home with venom into the roof of the net.
68' - GOAL FULHAM - Fulham's right-hand side inspires another fine attack; Kasami twisting away, introducing the overlapping Riether who swung a deep cross to Steve Sidwell at the far-post and the midfielder powered above Fox to net past Mark Bunn.
Steve Sidwell's goal is his third in successive matches for Fulham.
Norwich haven't won in 15 matches against Fulham, in all competitions.
Norwich are without a victory in eight matches, in all competitions.
TALKING POINT - Is Chris Hughton under pressure at Carrow Road? When does a manager officially become under pressure? Eight matches without a win seems reasonable to assess Hughton's impact at Carrow Road. Big money signings, such as, Johan Elmander and Ricky Van Wolfswinkel continue to disappoint, the team lacks invention in midfield and goals are drying up, especially if Gary Hooper isn't around. Of course, January brings the opportunity to freshen the ranks, but if business isn't done quickly - more than just Jonas Gutierrez - then you struggle to see where Norwich will find the quality to avoid a nail-biting end to the season.
MAN OF THE MATCH
Giorgos Karagounis (Fulham) - The Greek midfielder was fantastic for the Cottagers in the middle of the park. While not possessing such elegance on the ball as a playmaker, Karagounis was a vital cog, working all over the park, recovering second balls and in general, working the engine room of Fulham's side. A special mention, also, for his goalscoring midfield partner Steve Sidwell.
Fulham: Stekelenburg 6; Riether 8, Hangeland 6, Burn 6, Richardson 6; Karagounis 8, Sidwell 8; Dejagah 6, Kasami 6, Kačaniklić 6; Bent 7, Dembele 5, Christensen 5, Tomovic 5
Norwich City: Bunn 6; Whittaker 5, Martin 5, Bassong 6, Garrido 5; Fox 5, Johnson 6, Snodgrass 6; Redmond 5, Josh Murphy 7, Elmander 6, Van Wolfswinkel 6, Becchio 5.
THE MATCH IN A TWEET