The Toffees recorded their fourth successive home victory to boost their European ambitions as well as all but condemning Harry Redknapp's QPR to relegation
Goals either side of halftime from Darron Gibson and Victor Anichebe ensured the Toffees’ late surge to finish in the top four remains a strong one with just seven games remaining.
While Harry Redknapp’s QPR is now all but relegated as it suffered yet another defeat on the road, leaving the team seven points from safety.
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 created space for Junior Hoilett but his curling effort went narrowly wide of Tim Howard’s upright.
Victor Anichebe was once again preferred to the out-of-form Nikica Jelavic up front but he couldn’t get on the end of Leighton Baines’ wicked cross from the left before his in-swinging corner forced Julio Cesar into action for the first time.
Ji-Sung Park controlled a long ball brilliantly on the edge of the box and his square ball from the byline was met sweetly by the on-rushing Loic Remy but the Tim Howard reacted instinctively to push his goal-bound effort to safety.
Harry Redknapp’s side was once again left to rue its 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 defense simply couldn’t deal with the firepower of Everton's set-pieces and Cesar was once again forced to pull off a fine save to palm Distin’s header over the bar, before Anichebe doubled the lead before the hour mark.
Baines’ deep corner was met by the head of Distin, and his goal bound effort was flicked past Cesar by the big Nigerian striker.
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 Mirallas saw his volley from an impossible angle superbly kept out by Cesar.
As the minutes ticked down, QPR desperately tried to spark a comeback but the visitors lacked quality in the final third to cause any real problems to a resolute home defense.
Everton is now just three points adrift of Chelsea in fourth but the Stamford Bridge club has played a game less. David Moyes’ side visits the Emirates Stadium on Tuesday in what will prove to be a crucial game in the race for Champions League football.