The Toffees recorded their fourth successive home victory to boost their European ambitions, while Harry Redknapp's side face the drop after four matches without a win
Goals either side of half time from Darron Gibson and Victor Anichebe ensured the Toffees’ late surge to finish in the much coveted top four positions remains a strong one with just six games remaining.
Meanwhile, Harry Redknapp’s QPR are now all but relegated as they suffered yet another defeat on the road, leaving them sevens point from safety.
The Toffees welcomed both Marouane Fellaini and Steven Pienaar back into the starting line-up after the pair missed the last two games through suspension.
Redknapp opted to shuffle his pack after last week’s disappointing draw with relegation rivals Wigan. Ji-Sung Park replaced the suspended Bobby Zamora, while Esteban Granero and Nedum Onuoha were preferred to Stephane Mbia and Armand Traore.
It was the visitors who made the brighter start and went inches from taking an early lead. Some nice build-up play down the left including a brilliant solo run from Andros Townsend which created space for Junior Hoilett but his curling effort went narrowly wide of Tim Howard’s upright.
However, it wasn’t long before David Moyes’ side found their feet and a driving run from right-back Seamus Coleman ended in a loud penalty appeal from the Goodison Park faithful after Clint Hill clumsily felled the Irish international in the box, but referee Lee Mason waved away the claims.
As so often the case when you’re down at the bottom, the luck goes against you and Harry Redknapp’s side were once again left to rue their bad fortune as Everton took the lead with four minutes remaining in the first period despite the R’s having had the better of the play.
Kevin Mirallas’ initial shot was blocked into the path of Gibson on the right side of the area, and the midfielder’s powerful shot took a huge deflection of the Clint Hill to leave Cesar wrong-footed and helpless.
The QPR defence struggled to deal with Everton on set-pieces after the interval and Cesar was once again forced to pull off a fine save to palm Sylvain Distin’s header over the bar.
However, the resulting corner was sent deep into the box by Leighton Baines with Distin rising highest to meet the ball yet again before Anichebe flicked the centre-back's goal-bound effort past Cesar to extend the Toffees' lead.
With the R’s Premier League status hanging by a thread, Redknapp introduced Adel Taarabt with half an hour remaining but at the other end, the very impressive Kevin Mirallas saw his volley from an impossible angle superbly kept out by Cesar.
As the minutes ticked down, QPR desperately tried to pull a goal back and spark a comeback but the visitors lacked quality in the final third to cause any real problems to a resolute looking home defence.