Ross Barkley looked like a man intent on making up for lost time in his first start of the season, and fired an effort over the bar in the sixth minute before drawing Kieran Richardson into a foul on the edge of the box shortly afterwards.
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In the 18th minute Everton took the lead as Leighton Baines's wicked delivery was nodded home from close range by Jagielka, who has taken his tally to three goals in his last five games for Everton and England.
Villa were restricted to speculative efforts for the first half-hour, but Alan Hutton almost levelled with a left-footed strike from the edge of the box which curled just wide of the far post.
It was then the turn of Everton's right-back to come close, as his powerful drive was turned away by a sprawling Brad Guzan who ensured his side went into the break just one goal behind.