The hosts were in complete control throughout the match and were rarely troubled by their Championship opponents.
Ross Barkley opened the scoring on 35 minutes, slotting home on the left after clever work from Bryan Oviedo.
The lead was then doubled just before the break as Nikica Jelavic latched onto a mistake from Karl Henry and smashed the ball past Julio Cesar.
Jelavic grabbed a second on 68 minutes, guiding home Oviedo's cross, and missed the chance of a hat-trick moments later as his penalty hit the bar.
Seamus Coleman rounded off the scoring with a side-footed effort from 20 yards for his sixth goal of the season.
Here's a look at some Everton-related talking points to emerge from this contest.
Roberto Martinez made five changes for this game and left out the likes of Kevin Mirallas, Steven Pienaar and Romelu Lukaku; however, unlike in the Capital One Cup, he kept enough core players in key positions to dominate the opposition.
Everton also made five changes in their previous two Premier League games, simply as a result of the demanding fixture list.
The fact so many Premier League starters remained for this clash showed Martinez's respect for the competition—a stance that will be welcomed by Evertonians.
Gareth Barry and James McCarthy kept the Toffees in possession and moving at pace, while the likes of Leon Osman and Ross Barkley created enough in and around the final third to expose QPR.
Defensively, Everton played their strongest available unit, only resting the recently returned Leighton Baines, while Nikica Jelavic played in attack and got a chance to prove his worth to potential suitors.
Nikica Jelavic's decline in form has seen him become surplus to requirements under Roberto Martinez.
Since Romelu Lukaku's arrival, the Croatia international's played just 91 minutes of Premier League football across 16 games. He hadn't scored this season or in any of his last 18 appearances for the club; in fact, before this game he had scored only one goal in 30 games.
Many anticipate him leaving the Toffees in the coming weeks but, if that proves accurate, Jelavic gave the Goodison Park faithful a final chance to cheer his name.
His two-goal salvo already gave him as many goals in 2014 as he managed in all of 2013. It was his 20th and 21st strike in Everton colours coming in his 69th appearance, although a fluffed penalty prevented him grabbing a first hat-trick for the club.
If Jelavic does go, regardless of his persistent lack of form, many supporters will be sad to see him depart. His name was sung relentlessly by the home supporters throughout this match in what was possibly a farewell.
Ross Barkley has been one of the major success stories of Everton's season.
He's predominately played off the striker, where his strength and quick feet often open up a defence. He's also delivered some competent cameos in central midfield—a role he may ultimately feature in more as he matures.
In this game, however, he began on the left of Everton's trio of attacking midfielders.
After a slow start, Barkley became a constant menace to QPR, looking to cut in and shoot at every opportunity. That was exactly how his goal came about as he slotted home a precise finish to give his side the lead.
He linked up well with Bryan Oviedo, showing positional awareness of when to track back, and was one of the game's top performers.
The very best players have so many attributes they can prosper all over the pitch. Whether there's anything to this new role or not, it's further signs of Barkley's ability to flourish wherever he features.
Everton are currently without Phil Jagielka and Sylvain Distin, both of whom are sidelined by injury.
However, Antolin Alcaraz and John Stones played their second game together and once again produced accomplished displays.
Both are natural fits in a Roberto Martinez system: comfortable on the ball, able to pick a pass and bring the ball forward out of defence. Their presence helps the passing game become much more fluent in transition from the back.
They also suit each other's styles. Alcaraz is more prone to gliding forward and finding a pass, while Stones is more combative.
Both players have shown they are more than ready to perform for Everton and, once Jagielka and Distin return, Martinez will have some tough decisions to make.
The Catalan may even consider employing his favoured back-three at some stage in an effort to accommodate them.
Once again, Bryan Oviedo delivered a performance that makes him a hard man to drop.
Technically, Everton rested Leighton Baines to include the Costa Rican, but Oviedo was once again one of the most industrious and creative players on the pitch.
He grabbed two assists and contributed to a defensive effort that gave goalkeeper Joel Robles almost nothing to do.
Only Kevin Mirallas has more assists for Everton this season, despite Oviedo making just 10 starts.
If similar bids of £16 million start appearing for Leighton Baines, it's hard to see the logic of a financially troubled club rejecting them, especially with Baines now 29 and approaching the final year of his contract.
Still just 23, Oviedo has certainly proved himself a more than adequate deputy.
In dominating QPR, Everton produced their best defensive display in two seasons through their overall control of the game.
The visitors managed just three shots, none of which were on target—the fewest shots the Toffees have conceded in any game over the past two campaigns.
Last season's home clash with Fulham is the only time in the past two years that Everton's opponents haven't tested the goalkeeper.
This further highlights the performances of Everton's defenders and is exactly how Martinez wants his side to play.
This performance was the Toffees' most perfected attempt at enforcing his approach.