Playing their first top-flight match since 2004, Leicester left it late to deny Everton on Saturday, with Wood curling in from just inside the penalty area to delight the King Power Stadium crowd.
Everton, still reeling from the loss of Ross Barkley – who will miss six to eight weeks with a knee problem suffered on the eve of the campaign – started brightly and took the lead thanks to Aiden McGeady's stunning 20th-minute finish.
Record signing Leonardo Ulloa, who joined from Brighton and Hove Albion for a reported fee of £8million last month, provided a swift response within two minutes for Leicester, though.
With half-time looming, Everton took the lead again thanks to Steven Naismith's well-taken effort from inside the penalty area, but Wood's late strike ensured both sides would share the spoils.
Wood, who replaced Ulloa with 12 minutes to play, showed great composure to calmly slot past Everton goalkeeper Tim Howard and give Leicester a lift ahead of a tricky trip to Chelsea next week.
Leicester boss Nigel Pearson kept faith with the majority of players that won the club promotion from the Championship last term, with Ulloa the only new face to start for the hosts.
Everton begun brightly, controlling possession in the early stages, and Gareth Barry was influential.
Leicester responded with a spell of pressure but their opponents broke the deadlock thanks to McGeady's outstanding goal, which came after Pearson's men failed to deal with a corner from the left and follow-ups from Leighton Baines and Sylvain Distin.
From there, the ball fell to McGeady, who took a touch and - despite goalkeeper Kasper Schmeichel closing him down - curled an effort over three defenders, including Ritchie De Laet on the line, and into the top corner via the right post.
Leicester were not behind for long, though, as Ulloa marked his first start for the club by firing home from seven yards after Everton could not clear their lines from a corner.
McGeady and Naismith wasted chances to restore Everton's lead but the latter made amends in the final minute of the half, lashing a deflected cross from Baines into the back of the net to delight the travelling fans.
Neither side could match their first-half displays after the break, but substitute Jeffrey Schlupp did go close to equalising for Leicester.
A neat ball from Riyad Mahrez released the Ghana international behind the Everton defence but he could only blast over.
Schlupp's miss was soon forgotten, though, as Wood pounced with his late leveller.
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