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Everton made the brighter start to the match, and took the lead when Aiden McGeady picked out the top corner with a curling effort to score his first goal for the club.
However, their lead lasted just two minutes, when, after forcing a corner straight from the restart, Leicester equalised through a header for debutant Leonardo Ulloa.
It looked like the sides would be heading into the break level, but Steven Pienaar found Steven Naismith just before the break, setting up the latter for a shot which went in off the underside of the bar.
Leicester made a bright start after the break as they pushed for an equaliser, but they struggled to convert their possession into shots on goal.
Jeffrey Schlupp came off the bench to give the newly-promoted side some fresh legs up front, and he had a golden chance just moments after being introduced, but sliced his strike high into the stands.
Leicester continued to push for a goal, and managed to get back on level terms inside the final five minutes when Wood, who had been on the pitch less than 10 minutes, when tapped in at the near post.
Everton piled forward in the final moments as they tried to force a winner in stoppage time, but Romelu Lukaku fired the ball over with their last chance, ensuring that the scores finished level.