Ross Barkley capped off an inspired half with a superb individual strike on 33 minutes which sparked the game into life after an uneventful opening half hour on Merseyside.
Kevin Mirallas doubled the hosts’ advantage two minutes before the break as he curled a heavily-deflected free-kick off Eduardo Vargas and past Rob Green.
Barkley continued his influential performance in the second half and was involved in Everton’s third as Steven Naismith headed past Green in the Rangers goal to extend his side’s lead within 10 minutes of the restart.
Rangers lacked a real presence up front for the majority of the opening hour, prompting Harry Redknapp to bring Bobby Zamora on. And having given his side a bit more bite up front the striker reduced the deficit 10 minutes before full-time, converting from close range after Tim Howard had parried Jordon Mutch’s shot.
That, coupled with a nasty-looking injury to Mirallas in the closing minutes, was the only bad note on what was otherwise a great performance from Roberto Martinez’s side as they leapfrogged Liverpool into 10th in the Premier League, while QPR’s eighth consecutive away defeat leaves them in the bottom three, a point adrift of Burnley.
QPR had arguably made the brighter start, with Matt Phillips guiding a tricky volley just over the bar and Junior Hoilett shooting straight at Tim Howard.
The home fans were unhappy with the hosts’ slow start but saw signs of the sort of play Goodison Park has become accustomed to in the 26th minute when Coleman broke down the right and crossed for Naismith, whose shot was inadvertently blocked by Romelu Lukaku.
And seven minutes later the hosts took the lead through a moment of individual brilliance.
Barkley picked up the ball by the halfway line and drove forward before unleashing a shot that arrowed into the top corner via a slight deflection off Mauricio Isla.
And just 10 mintues later they doubled their lead after Joey Barton gave away a free-kick for catching Naismith with a trailing elbow and, from the resulting free-kick, Mirallas’ shot deflected off Vargas and beyond Green.
Vargas had enough time to get a deliberate touch but he could not have directed the ball into a worse position as far as his team and ‘keeper were concerned.
Everton were buoyed by their lead and almost managed a third before half-time, but this time Aiden McGeady’s curling effort was just past the far post.
QPR had never recovered from a two-goal half-time deficit in the Premier League and they showed no sign of achieving that once the second 45 got underway.
The opening moments of the second half saw Mirallas appeal for a penalty after Richard Dunne put his arm across the Belgian but with contact appearing minimal referee Neil Swarbick waved the claims away.
But the pressure soon told as the Toffees capitalised on a misplaced clearance from Green in the 53rd minute.
Mirallas played in McGeady on the right and his cross found Naismith in yards of space to head the ball in despite the efforts of Nedum Onuoha and Dunne on the line.
With that, Redknapp introduced Zamora and, with Everton appearing to ease off the gas, Rangers had some prolonged joy for the first time in the game.
In the 80th minute Howard could only parry Mutch’s shot straight to Zamora, the striker duly converted from six yards to reduce the arrears and bag his first goal of the season.
The home fans were becoming frustrated as the game meandered to its conclusion, a conclusion which had a sour ending for the hosts as Mirallas was carried off after Mutch’s poor challenge.
The Belgian turned his ankle under the tackle from Mutch and appeared to be in some discomfort when he was carried from the field and replaced from Arouna Kone.
The Ivorian made his second appearance since returning from injury himself and his first league appearance in a year.
And Kone almost turned provider after he slipped Samuel Eto’o in in the closing stages but the veteran striker’s effort struck the post just moments before the full-time whistle.
Everton: Howard (6), Coleman (7), Jagielka (6), Distin (5), Baines (5), Barkley (9), Besic (8), McGeady (7), Naismith (7), Mirallas (7), Lukaku (5).
Used Subs: Eto’o (7), Kone (4), Pienaar (5).
QPR: Green (6), Isla (5), Dunne (5), Onuoha (5), Yun (6), Phillips (4), Mutch (5), Barton (6), Fer (5), Hoilett (7), Vargas (5).
Used Subs: Kranjcar (3), Zamora (6).
Man of the Match: Ross Barkley
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