A 17 minute second half hat-trick from Andre Schurrle sealed the three points, with Fulham's goal coming from Johnny Heitinga.
Elsewhere, Arsenal's Premier League title challenge suffered a huge blow, as they went down 1-0 to Stoke City at the Britannia Stadium.
Irish international Jonathan Walters scored the winner for Stoke from the penalty spot.
Newcastle United boss Alan Pardew was sent to the stands during his side's 4-1 win away to Hull City at the KC Stadium.
He could be in big trouble with the FA after the referee sent him off following a confrontation with Irish international David Meyler.
On the pitch, Moussa Sissoko scored a brace for Newcastle, while Loic Remy and Vurnon Anita also netted.
Curtis Davies scored Hull's goal.
And Romelu Lukaku scored late on to give Everton a 1-0 win over West Ham at Goodison Park that revives their European hopes.
