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The visitors came out of the blocks at a blistering pace and it paid off straight away, as Lukaku capitalised on a Jonas Olsson error to rifle home from 18 yards with only two minutes on the clock.
Albion looked rather toothless in the opening half despite sharing some encouraging possession, and Craig Gardner could only send his long-distance effort over the crossbar. The midfielder later sent a free kick from a promising position straight into the Everton wall.
The Toffees could have extended their lead against the run of play as the half drew to a close, when Kevin Mirallas found space before sending his shot just high over the bar from 20 yards out.