The 25-year-old had scored two and assisted two for Garry Monk’s men since the Championship season got back under way, and Murphy – who entered the fray as a half time substitute for Moses Odubajo at Craven Cottage – again made an eyecatching impact in West London.
A brace from former Newcastle man Aleksandar Mitrovic and a strike from Neeskens Kebano had given the hosts a commanding lead at the break, but Murphy won a penalty which Atdhe Nuhiu converted to cut the deficit.
Another Kebano effort made it 4-1 but on-loan United winger Murphy responded for Wednesday as his deflected drive found the target.
Murphy then provided another assist for Nuhiu’s second in the dying moments to set up a tense finale, but Bobby Decordova-Reid’s clincher in added time made sure of Fulham’s win, even though Harrison Reed saw red late on.
That means Murphy now has eight goals and six assists to show for his time at Hillsborough this term, with the Owls dropping to 16th in the second tier ahead of their final outing of 2019/20 against Middlesbrough.
Meanwhile, goalkeeper Freddie Woodman’s missed just his second Swansea City game this season as Steve Cooper’s side beat Bristol City 1-0 at the Liberty Stadium.
The victory keeps the Swans’ play-off hopes alive, but Woodman, who missed out with a hip problem for the second game in succession, was replaced by Erwin Mulder for the victory, which keeps them in with a shout of a place in the top six.
Achraf Lazaar’s Consenza also won on Friday, beating Pordenone 2-1 away in Serie B.
Former United frontman Emmanuel Riviere netted Cosenza’s first of the evening, but full back Lazaar remained an unused substitute.