Andy Johnson's first-half opener had been cancelled out by Shola Ameobi before Murphy settled the game from the penalty spot as Joe Kinnear's side endured another fruitless trip to the capital.
Fulham boss Roy Hodgson kept faith with the team that was narrowly beaten by Everton last weekend and his side enjoyed the better of the opening exchanges as Jimmy Bullard, Murphy and Zoltan Gera all came close to breaking the deadlock.
The home side got the goal their play deserved on 23 minutes thanks to a defensive error by Claudio Cacapa.
Bullard swung in a cross from the left wing but the Brazilian could only head the ball against his fellow South American Fabricio Coloccini.
The ball fell kindly for Johnson, who claimed his third goal in two games with a firm eight-yard strike past Shay Given.
Newcastle began to exert some pressure of their own as the half wore on. Obafemi Martins collected Ameobi's knockdown but could only fire wide and Damien Duff was unlucky to see his right-footed effort come back off the post after showing a good turn of pace to beat Paul Konchesky.
But the visitors were level ten minutes after the restart. Duff's deflected cross caused mayhem in the Fulham box, allowing Ameobi to finish from close range with the crowd screaming for offside.
Hodgson responded by replacing Gera with Clint Dempsey and was rewarded with a penalty two minutes later.
Johnson burst into the box and went down under a clumsy challenge from Coloccini, with referee Martin Atkinson pointing straight to the spot. Fulham captain Murphy stepped up to slot home the penalty.
Kinnear brought on Michael Owen for the closing stages and the former Liverpool star should have equalised with ten minutes remaining. However, he failed to convert from six yards with England coach Fabio Capello watching in the stands.