Hugo Rodallega, who famously netted at Stoke City to preserve Wigan Athletic's top-flight status in 2011, was rewarded with a start by Fulham boss Felix Magath after sealing last weekend's 2-1 win at Aston Villa.
The Colombian striker once again proved himself adept amid a scrap for survival as he stole in to score the only goal five minutes before half-time.
Fulham were indebted to goalkeeper David Stockdale for a pair of magnificent saves, while Norwich - playing for the first time under club stalwart Neil Adams after Chris Hughton's sacking last Sunday - also struck the crossbar through Robert Snodgrass.
But Magath's men played with greater assurance after taking the lead and are now just two points behind fourth-bottom Norwich, who face a daunting final four games against Liverpool, Manchester United, Chelsea and Arsenal.
Stockdale endured a nervy moment in the sixth minute, pushing behind as Nathan Redmond – one of six new faces in the starting XI selected by Adams – launched a right-wing cross that threatened to sneak in at the near post.
Rodallega carried the major attacking threat for the hosts during a disjointed opening.
He pulled a shot across the outstretched John Ruddy and past the far post after Pajtim Kasami's flick on, before nodding tamely at Norwich's goalkeeper when Steve Sidwell diverted a 19th-minute punt into his path.
Stockdale was soon handed some considerably more taxing work and responded with a pair of outstanding stops.
Ricky van Wolfswinkel was ready to celebrate the end of a 23-game goal drought when he volleyed goalwards from Jonathan Howson's cross, but Stockdale produced a stunning reaction save.
From the resulting 29th-minute corner he kept out Leroy Fer's powerful header before Bradley Johnson lashed the rebound wastefully wide.
Stockdale could do nothing as a Snodgrass free-kick cannoned back off the bar and, buoyed by those reprieves, Fulham took a 40th-minute lead.
Norwich full-back Steven Whittaker rashly brought down Kieran Richardson and some horrible marking allowed Sidwell to glance on Lewis Holtby's left-wing delivery for Rodallega to sweep home on the half-volley.
Van Wolfswinkel's plummeting confidence levels were underlined when he inexplicably gave away possession when well placed inside the Fulham area as Norwich sought a second-half response.
But the visitors' set-piece frailties almost undermined them again as Rodallega met a 55th-minute corner to be denied by Martin Olsson on the line.
Meanwhile, Fulham's defence were covering themselves in glory - centre-back Fernando Amorebieta launching a brave last-ditch challenge to deny Snodgrass after the lively Redmond touched the ball beyond the previously impenetrable Stockdale.
Even Rodallega was influential in his own area, heading Michael Turner's goal-bound effort to safety, while substitute Scott Parker and fellow midfielder Sidwell came close to giving Fulham breathing space within the last 20 minutes.
Norwich were relegated following a 6-0 drubbing at Craven Cottage nine years ago. Despite substitute Ashkan Dejagah spurning a glorious chance to rub salt into City's wounds, this result could prove just as decisive in the final reckoning.
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