QPR had their chances in the opening stages, with Loic Remy forcing Tim Howard into a fine save, but they were made to pay for not taking their opportunities, as Darron Gibson's deflected strike gave the Toffees the lead at the break.
The interval seemed to revitalise the home side, who came out of the blocks with far greater intensity, and almost doubled their lead, when Victor Anichebe hit the post from close range.
However the dogged striker did find the net soon after to seal a comfortable win for the Toffees, making it four home wins in a row, pushing QPR further towards the dreaded drop.
After a slow start, where the conditions hindered much of the better attacking play, Howard produced a moment of brilliance to deny Remy giving QPR a deserved lead.
The Frenchman expertly found space in the box from Park Ji-sung pull-back, side-footed the ball goal-wards, but the American stopper stuck out a left hand to palm the ball wide.
That instinctive save proved even more vital as the Toffees took the lead in fortuitous circumstances.
Kevin Mirallas' effort was blocked after neat work down the left from Leighton Baines, the ball fell to Gibson who drilled an effort towards goal, which Julio Cesar looked to have covered, but Clint Hill stuck out a leg and deflected the ball past the despairing keeper to give the home side the advantage at the break.
The second-half was all one-way traffic, and the Merseysiders should have doubled their lead five minutes into the half.
Mirallas did brilliantly to get to the byline, pulled the ball back to Anichebe, who had an age to pick his spot, but saw his attempt come back off the inside of the post.
However, it wasn't long before the tireless hitman found his scoring touch, flicking the ball past Cesar after Sylvain Distin had headed an in-swinging corner from Leighton Baines into his path.
The second goal seemed to kill off any hope the Rs had, and it was all too easy after that for David Moyes' men.
Howard produced a couple of other fine saves, but QPR just did not offer enough going forward, and now face a uphill battle to remain a Premier League side next season, whilst Everton now boast a five-point gap over bitter rivals Liverpool with a game in hand.