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Marouane Fellaini headed the Toffees ahead with his 12th goal of the season late in an evenly-fought first-half, in which Reading hit the woodwork, and the Merseysiders eased to victory after the break.
Defeat left Reading in the bottom three and in the thick of a battle for survival while Everton, after last week's disappointing loss at Norwich, could still entertain hopes of finishing in the top four.
To their credit, Reading battled on, even if only to reduce the damage to their goal difference column.
Mucha made a good save from Jobi McAnuff and the visitors did pull one back six minutes from time as Harte crossed from the left and an unmarked Robson-Kanu headed home with conviction.