Michel Vorm had the nickname 'Penalty Killer' in his native Holland, and the Swansea goalkeeper added to his growing reputation with a crucial save to steer Brendan Rodgers' side to victory.
Vorm guessed the right way for the second time this season – the first was against Wigan in August – to save Clint Dempsey's 87th-minute spot-kick after Jazz Richards had brought down Karim Frei.
It allowed Swansea to jump into the dizzy heights of 11th place and Rodgers, their manager, said: "Any good goalkeeper would get you up to 10-plus points. That penalty was a key moment, although it wasn't a penalty. If you look at the replay you can see that Jazz Richards doesn't do anything and the guy kicks his leg, goes over and the referee bought it.
"But as for the save, you see so many goalkeepers try and steal two or three yards off their line but he was near enough to his line going the right way and used a strong arm , and that was as much as we deserved because we were the side always trying to make the breakthrough."
The contribution of Vorm came between second-half goals from Scott Sinclair and the substitute Danny Graham, who sealed the win deep in injury-time from Mark Gower's corner. Yet it was Sinclair's fortunate 56th-minute strike – aided by a wild deflection off Clint Dempsey – which set Swansea on their way.
After Wayne Routledge's miscued shot landed in his path, the former Chelsea winger's goalbound effort was deflected by Dempsey past the Fulham goalkeeper, Mark Schwarzer, into an empty net.
The win was Swansea's second in eight games but it is Fulham who now lie only four points above the relegation zone and Martin Jol's decision to drop the striker Bobby Zamora will come under scrutiny. The pair have had a frosty relationship since the Dutchman took charge at Craven Cottage last summer.
But Jol played down any suggestion of a new rift with Zamora and said he had been fully justified to select Andy Johnson over Zamora, after watching the players in training last week.
Jol said: "I made a decision on Thursday to play Andy Johnson because he works hard in training. In the last couple of weeks we have played [Moussa] Dembele and Bobby together but I thought it was time to play Andy again. Bobby didn't travel because he's not a player who is the best to be a substitute. It's happened before.
"Sometimes I make a decision for the club. I made a decision to play Andy Johnson and I told [Bobby] I wouldn't take him to Swansea. I thought it was better to wait until next week as we have important games coming up. I need all my players."
Zamora, who has not scored since 2 October, has been substituted in Fulham's last four matches amid reports that Queens Park Rangers are interested in singing the former Spurs and West Ham man. Jol said: "I don't have any problem with any player. The only thing I want is for players to give 100 per cent to the club. I still feel he wants to play for this club."
Without Zamora, Fulham came to life once they fell behind, and then they found Vorm in inspired form. The former Utrecht man made saves from Bryan Ruiz, Dempsey and Johnson and John Arne Riise went close with a thunderous free-kick.
Swansea could have extended their lead sooner, when Kemy Agustien cracked the post with his first touch, before Graham added the gloss to the win with his fifth goal in the Premier League, courtesy of a neat flicked finish.
Rodgers said: "It's a great win for us and it was what we deserved. Fulham are established side at this level. We had to be patient but it's another clean sheet, which is seven in 15 games."
Swansea (4-3-3): Vorm; Richards, Caulker, Williams, Taylor; Britton, Gower, Moore (Agustien, 69); Routledge (Dyer, 89), Lita (Graham, 76), Sinclair.
Fulham (4-4-2): Schwarzer; Kelly, Hangeland, Senderos, JA Riise; Ruiz, Etuhu, Davies (Sa, 79), Dempsey; Johnson, Dembele (Frei 77).
Referee: Jonathan Moss.
Man of the match: Vorm (Swansea).