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.
Bobby Zamora pulled a goal back with 10 minutes left, but the damage had already been done, with defeat for Harry Redknapp's side ensuring they are still without a point away from home this 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.
