Roberto Martinez has made a habit of making match-defining substitutions for the Blues this term.
And it was his trio of changes that transformed this contest and ensured Everton's European mission remains well and truly on track with just seven games of the campaign remaining.
After a lacklustre and goalless opening period, the half-time introduction of Steven Naismith
paved the way for the opening goal - an unfortunate own-goal for the otherwise impressive David Stockdale.
Fulham turned up the heat in search of the points to save their Premier League status and levelled themselves with 20 minutes remaining through sub Ashkan Dejagah.
But the Everton chief had more trump cards up his sleeve. Kevin Mirallas
and Aiden McGeady
entered the fray and combined to restore the lead with 12 minutes left.
Naismith's late third helped to wrap up the points - and leaves the Blues four points behind fourth-placed Arsenal with a game in hand and the Gunners the next visitors to Goodison Park.
Martinez has now made 13 goal-scoring substitutions for Everton this term. Impressive indeed.
A run and shot inside the opening 90 seconds from Lukaku seemed to set the tone for Everton's intent for the afternoon - and suggested match-winning subs wouldn't be required.
But Fulham's high-pressure approach denied the Blues the space they craved in the heart of midfield in the early stages and meant much of the ball was played across the backline by the visitors during the opening 15 minutes of the contest as they patiently probed for a foothold in the game.
By contrast, there was a frenetic approach to Fulham's play - understandable given their league predicament.
After some early range-finders from Holtby and Kasami inside the opening 10 minutes, the home side created a couple of good chances in a crowded area as they pressed the visitors.
A Brede Hangeland header wide was the closest they came to beating Tim Howard
during the opening 20 minutes of the contest though.
As the game developed, and the home side pressed harder, it created space and openings for the Blues on the counter. And inside a frantic 60 second period midway through the opening half Tim Howard
and David Stockdale were called into action at either end, with Kieran Richardson and Gerard Deulofeu denied respectively.
A Holtby headed effort again forced Howard into action as the home crowd became increasingly vocal - in supporting their team and displaying their frustration with the match officials.
The team they were backing continued to have the lion's share of the chances in the first period. But efforts from outside the box from Holtby, Sidwell, Dembele and Riise were all very high and very wide.
At the other end, Barkley was far more accurate from similar distance but his 36th minute effort didn't prove a difficult test for Stockdale.
The best chance of the first period didn't materialise until injury-time, Howard gathering a header from Moussa Dembele at close range.
Barkley, who appeared to be limping when he left the field at the break, was replaced by Scotland international Naismith for the second 45 minutes. And it was to trigger the change in fortunes Everton craved - and needed.
The sub made an instant impact. His lively running and neat inter-play on the edge of the box resulted in a great low cross which earned a corner. And minutes later he latched on to the loose ball from a corner to send a shot goalwrds which was deflected twice - the final time off the keeper's feet - before finding the back of the net.
Lukaku tested Stockdale seconds after the restart as the Blues found their feet and attacking gusto. And much of the eye-catching attacking link-up play had the effervescent Naismith at the heart of it.
A stunning pass from him set Baines free on 59 minutes but the full-back's effort flashed wide with Lukaku lurking.
Lukaku was denied himself on 64 minutes after a period of sustained Everton pressure.
But in a game that had been ignited by an improved second half display from the visitors, Fulham responded. And they found an equaliser through substitute Ashkan Dejagah with 20 minutes to play. It was a fierce right-footed drive from the edge of the box after he had cut inside from the left flank.
It made for a tempestuous, tense and enthralling final period of the game.
Howard made a superb point-blank save to deny a Dembel header and that was quickly followed by another stop from Kasami as the home side's hopes grew.
At the other end, sub Aiden McGeady
showed some neat footwork before centreing a cross which James McCarthy
volleyed agonisingly across the face of goal and wide.
But the agony didn't last for long. Roberto Martinez introduced Aiden McGeady
and Kevin Mirallas
as like the first sub, the duo made a telling impact on the contest.
McGeady sent a lovely ball into the path of Mirallas with 12 minutes left on the clock and the Belgian made no mistake as he charged into the box.
A superb pass from Lukaku released Naismith in the 83rd minute but as the Blues sought a third goal to give them a two goal cushion, Stockdale was equal to the Scot's effort.
But he could do nothing to prevent the tap-in he was presented with five minutes from time after a succession of close calls and scuffed passes finally resulted in the ball falling to the forward's feet six yards from goal.
Naismith struck the woodwork in the 90th minute as the visitors continued to probe for more goals. But a fourth wasn't needed.
The Blues move on to 60 points - five short of their best ever Premier League haul with seven games still to play. This season could yet get very, very interesting.