The goals were undermined by frustration and this could prove to be a fitting end for Nikica Jelavic at Everton as the Croat wasted his chance of a hat-trick by chipping a penalty on to the bar.
His career at Goodison Park started with 10 goals in 10 starts after he joined from Rangers two years ago but he could join QPR or West Ham in the coming days as he looks for regular football before the World Cup after enduring a disappointing season and a half.
Bookended by goals from Ross Barkley and Séamus Coleman, Jelavic's goals either side of half-time equalled his tally for the whole of 2013. But after Bryan Oviedo went down under Nedum Onuoha's challenge in the area with the score at 3-0, Jelavic clipped his shot from the spot on to the woodwork. And as well as the tinge of embarrassment, he received a dressing down from QPR's goalkeeper Júlio César for his cheek.
Roberto Martínez, who won the FA Cup with Wigan last year, has made it clear that Jelavic, 28, will be available only for a permanent move but maintains it would be wrong to assume that the forward will definitely be on his way.
"His performance was very, very good," said the Everton manager. "You have to understand he's frustrated that he didn't get the hat-trick his performance deserved. His movement was terrific and he's been working really well in training. I don't want to sell Nicky and I don't want to lose him but I understand it's a key moment. If the World Cup wasn't there in the summer, it wouldn't be the case."
Everton were always in control but took more than half an hour to find a way past César, who was playing his first Rangers game of the season, despite remaining Brazil's first-choice goalkeeper. Barkley curled in from the edge of the area after a sweeping passing move before Jelavic thumped in a minute before the break after Karl Henry had given possession away.
Jelavic stabbed in from Oviedo's cross for the third and Coleman drove in a fourth from a wide position from Barkley's pass after Jelavic had squandered his penalty chance.
The QPR assistant manager Kevin Bond said: The Croat was also denied a third by an impressive block on the line from QPR defender Clint Hill.
"For us to change it we needed to come in at half-time at 1-0 and the goal just before half-time almost settled it as a contest."