Leandro Bacuna opened the scoring with a calm finish after linking well with Villa forward Christian Benteke.
Below, Sports Mole takes a look at the key talking points from the match.
On target: 6
On target: 1
Was the result fair?
The match statistics tell you everything you need to know from Goodison Park. Everton were dominant for long spells of the game and deserved to come away with three points, despite being frustrated for much of the contest. Roberto Martinez's side remained patient and were rewarded for persisting with their style of play.
Martinez saw his side pass the ball just as they normally do, but it proved to be a very difficult afternoon for the men in blue. Bacuna's goal came against the run of play and forced Everton into a tricky spot as they struggled to break down a stubborn Villa defence. They increased the tempo of their passing after the break and added a cutting edge to their play to complete an impressive fightback.
Paul Lambert would surely have been lost for words in the away dressing room after the game. Villa came to Merseyside with a clear gameplan and it seemed to be working perfectly after Bacuna handed them the lead. They pressed superbly in midfield and Ron Vlaar led a determined visiting defence. However, they were punished for dropping too deep in the second half as Everton took advantage of the lack of an attacking threat from the away side.
Sports Mole's man of the match
Steven Pienaar: The South African needed only 45 minutes to win this award, but very few players were anywhere close to matching his second-half display. Martinez was forced to turn to his bench at the break and Pienaar delivered an excellent performance filled with clever touches and tricky runs. His assist for Naismith's equaliser was very, very special.
Naismith may have scored one of the goals but he also must take some blame for not securing the win much sooner. After helping Everton come from behind to take the lead, the Scot had a great opportunity to double his personal tally when he found some space inside the box. However, Naismith headed straight at Brad Guzan from just a few yards out and the nervous wait continued. Thankfully for Everton fans, the miss did not come back to haunt them.
Robert Madley wasn't asked too many difficult questions on a routine afternoon at the office. The referee was only asked to produce a card on one occasion as he attempted to keep the game flowing as much as possible.
Everton: The Toffees face a trip to the capital next Sunday to face Tottenham Hotspur.
Villa: Lambert will be desperate to get back to winning ways when Villa host West Ham United next Saturday.