Ross Barkley scored a stunning long-range strike to break the deadlock after a quiet first half hour before Kevin Mirallas and Steven Naismith added the gloss to a comfortable win
Barkley had not scored for the Merseyside club this season, but the precocious midfielder got off the mark in style with a sublime individual strike to put Roberto Martinez's side in front just after the half-hour mark at Goodison Park.
Kevin Mirallas doubled Everton's lead with a free-kick that took a wicked deflection off Eduardo Vargas shortly before half-time.
Steven Naismith then marked his return from injury by adding a third goal with a header early in the second half, as Everton moved above neighbours Liverpool into 10th place with only their second win in seven top-flight games.
|VIEW FROM GOODISON PARK
|By Tom Maston
Everton are back to winning ways, though they will have few simpler tests than that posed by a toothless QPR.
Harry Redknapp will no doubt point to Charlie Austin's absence as a major reason for their disappointing showing, but the Rs cannot survive if their away performances continue in this vein. They, more than most, need some steel adding during the transfer window.
For Everton's part, Steven Naismith gave them some much-needed impetus on his return from injury while Ross Barkley thrived in a slightly deeper role, with his superb individual strike an illustration of just what he can be capable of when given space to run into.
The home crowd may have been less than pleased with some of Roberto Martinez's sides defensive passing, but the Toffees are at least back moving in the right direction. A Champions League berth still looks a long way off, but with players back from injury they should be back in the race for a European place by the end of the festive season.
Naismith was passed fit after missing five games due to a hamstring injury, while Barkley and Aiden McGeady were also restored to Everton starting line-up.
Vargas was employed as a central striker in the absence of QPR's leading scorer Charlie Austin through suspension, with wingers Matt Phillips and Junior Hoilett making rare starts as Redknapp opted for a change of formation.
Rangers started with confidence and Phillips had a chance to mark his recall with an early goal, but failed to control a tame shot that looped over the crossbar.
Disgruntled Everton fans soon let their frustration be known after a lacklustre start and the home side responded, with Naismith's effort striking Lukaku after Seamus Coleman cut the ball back before Mirallas cut in from the left and let fly with a well-struck shot that flashed over the bar.
Barkley then provided the urgency the home side had been lacking when he produced a moment of class to put them in front 12 minutes before the break.
The England midfielder was on the halfway line when he played a one-two with Lukaku before surging forward and unleashing a venomous left-footed strike that gave Robert Green no chance.
Everton then stunned QPR with a second goal 10 minutes later, as Mirallas' free-kick struck Vargas and a wrong-footed Green could only watch on as he was beaten once again.
Mirallas went down in the penalty area under pressure from former Everton defender Richard Dunne just after the break, but referee Neil Swarbrick waved play on.
The home side added a third goal when 53 minutes in, when McGeady stood a cross up to the back post.
Green got a hand to Naismith's goal-bound header, but could only palm the ball against Nedum Onuoha and into the net.
It was another harsh lesson on the road for the London club, but they did at least pull a goal back when Zamora was on hand to turn the ball home after Tim Howard could only palm Jordon Mutch's shot into his path 10 minutes from time.
It was too little, too late for Redknapp's side, though, and Everton substitute Samuel Eto'o nearly added further gloss to the scoreline when he hit the post in injury time.