However, substitutes Mirallas and Naismith intervened in the closing stages to condemn the Cottagers to their 23rd defeat of the campaign.
Below, Sports Mole has looked back over the 90 minutes plus stoppage time to determine if Everton were deserving victors, or whether the win flattered them.
On target: 8
On target: 7
Was the result fair?
Looking at the statistics above, you would believe that Fulham were at least worthy of a point. The truth is, although they did create a handful of chances, they were wasteful, while Everton were clinical. For that reason alone, you'd have to say that although harsh on the hosts, the Merseysiders were deserving winners.
For 45 minutes, you would not have believed that Fulham were bottom of the table with the real threat of relegation looming over them. They carved out some openings of not and defended, by and large, well. However, they couldn't score when they were on top and when Everton pushed forward after the restart, the defensive frailties that have hampered Fulham all season raced to the surface. Their remaining three home matches are favourable and if they perform how they did during the first half, they may get some joy. It's got to be said, though, that safety looks to be almost out of reach for Felix Magath and his players.
Roberto Martinez will not have been a happy manager during the interval. Aside from the lively Gerard Deulofeu, in an attacking sense, Everton were slow and wasteful in possession. However, credit to Martinez because his three substitutes - Mirallas, Naismith and Aiden McGeady - all made an impact on the match. With Arsenal to come, confidence is bound to be high among the playing squad at Goodison Park.
Sports Mole's man of the match
John Stones: In seasons gone by, Everton would have missed the influence of Phil Jagielka at the heart of their defence. In recent weeks, though, 19-year-old Stones has stepped up to the plate. Today he not only showed good defensive awareness to make a host of clearances, but when the opportunity presented itself, the youngster displayed composure on the ball to start off numerous attacks. It was a really mature performance from the teenage centre-back.
Sadly for Fulham keeper Stockdale, this was one for the howler DVDs. First of all he attempted to meet a corner which he got nowhere near, but worse was to come. As Stockdale made his way back towards his line, Naismith shot from the edge of the area and after a deflection, the ball struck the retreating Fulham shot-stopper, before it crept over the line.
These two sides are by no means the most physical in the Premier League, so it wasn't expected to be a tricky afternoon's work for Anthony Taylor. That school of thought was proved to be a correct one, although when an offence did warrant a yellow card, Taylor didn't hesitate to correctly brandish one.
Fulham: Next Saturday the West Londoners travel to Birmingham for a clash with Paul Lambert's Aston Villa.
Everton: Meanwhile, a day later, the Toffees will play host to Arsenal at Goodison Park.