A goal from Steven Naismith looked to have given Everton all three points, before Wood struck in the closing minutes to ensure that the match finished level.
Here, Sports Mole takes a closer look at the events that unfolded at the King Power Stadium.
On Target 3
On Target 3
Was the result fair?
On the balance of play, Everton deserved to take the three points today. They were in control of the match for long periods and dominated possession. It had looked as if they would win before Wood's late goal, but a lack of concentration at the back cost them. Meanwhile, Leicester will be pleased to have salvaged a point on their long-awaited return to the top flight. They showed great fighting spirit to come from behind twice and their fans will have been delighted at the effort from their players this afternoon.
Leicester City's performance
The Foxes were not overawed in their first match in the Premier League for more than 10 years, but it was clear that they were playing against a team with more quality than they possessed. They surrendered possession far too cheaply in the midfield and struggled to deal with Everton's attacking threat, particularly from the left-hand side of the pitch. However, they never gave up and showed the passion and courage needed to survive in the top flight, while a goal from debutant Leonardo Ulloa will have been another positive for their manager Nigel Pearson.
Under Roberto Martinez, Everton have played some fantastic football and they showed glimpses of their quality this afternoon. Midfielders Steven Pienaar and McGeady looked a threat, while Naismith also enjoyed a fine outing. They were unable to get Romelu Lukaku into the game as much as they would have liked, but that had more to do with the striker's fitness following his late return from the World Cup. One thing that the manager will have been frustrated with is the poor defending that led to Leicester's equalisers. It was certainly uncharacteristic of them to concede such sloppy goals, given their fine defensive record last season.
Sports Mole's man of the match
Aiden McGeady: The Republic of Ireland international was the most dangerous player on the pitch today. He was always looking for the ball and the home defence struggled to keep up with his well-timed runs. A stunning curling effort into the top corner gave Everton the lead - his first goal for the club since joining from Spartak Moscow in January.
With Leicester trailing 2-1, they were given a great chance to level when Jeffrey Schlupp was sent clean through on goal. The Ghana international only had Tim Howard to beat, but he fired his effort high over the bar. It was a terrible miss at a crucial stage in the game and he must be a relieved man that his team did manage to equalise late on.
Mike Jones did not have the most difficult of matches to officiate. It was played in a good spirit, between two teams that looked to play football the right way. The referee only handed out a couple of bookings in the second half, for two clumsy, rather than malicious, tackles.
Leicester City: The Foxes face another tough match against Chelsea in the Premier League at Stamford Bridge next Saturday.
Everton: Martinez's men will welcome Arsenal to Goodison Park in next Saturday's Premier League clash.