Ross Barkley's stunning strike set Everton on their way to a Barclays Premier League victory as QPR's struggles away from home continued on Monday.
Barkley had not scored for the Merseyside club this season but the 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 - although he was stretchered off late on with an ankle injury.
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 their second win in seven top-flight matches.
Bobby Zamora pulled a goal back with 10 minutes left but the damage had already been done, with defeat for Queens Park Rangers ensuring they are still without a point away from home this season.
Naismith was passed fit after missing five matches due to a hamstring injury, while Barkley and Aiden McGeady were also restored to Everton’s 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 starting 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.
The home side responded after a lacklustre start and with Naismith's effort striking Lukaku after Seamus Coleman cut the ball back before Mirallas 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 the ball hit the back of the net.
The home side added a third goal when, 53 minutes in, 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.
QPR did at least pull a goal back when Zamora was on hand to turn the ball home after Tim Howard diverted Jordon Mutch's shot into his path 10 minutes from time.
It was too little, too late for Harry 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.
Everton manager Roberto Martinez: "The difference today was how clinical we would be in front of goal and I'm pleased with that. The first goal [from Barkley] is as good as it's going to get in terms of individual quality and how to break lines of pressure. The big encouragement working with Ross is how quickly he takes new concepts on."
On Mirallas: "Kevin is the real negative, he has a really bad ankle. We will scan it in the morning and it was a real disappointment to see him carried off at the end."
QPR manager Harry Redknapp: "I thought we played OK for 35 minutes or whatever it was. I thought we were comfortable and had good control. The first goal a great bit of play from Barkley, but took a deflection, and then obviously the free-kick as well.
"We kept going, but we needed a goal. The Everton crowd was edgy, I thought if ever there was a time we could come here and get a result this was it. I wasn't disappointed with how we played, I thought we played OK tonight. I was pleased with the performance. We pressed them well, worked hard and deserved more than we got from the game."
|20 Dec 2014||v Southampton (A)|
|26 Dec 2014||v Stoke (H)|
|28 Dec 2014||v Newcastle (A)|
|01 Jan 2015||v Hull (A)|
|10 Jan 2015||v Man City (H)|
|19 Jan 2015||v West Brom (H)|