Paul Lambert's men have been struggling in the Premier League and had not won since the last time they were on Merseyside to play Liverpool in December.
The Villans looked on course for victory until the 70th minute, when Marouane Fellaini scored to make it 3-2. The Belgian then struck again in injury time to seal a point for the Blues.
Here, Sports Mole takes a closer look to see if the result was fair.
On Target: 8
On Target: 2
Was the result fair?
It's cruel on Villa. They were the better team for most of the match, but as they dropped deeper their defending became sloppy. Nerves clearly played a factor as Everton finished strong.
6/10. The Toffees did not gel today and looked short on ideas and confidence. Steven Pienaar had a quiet game, while Marouane Fellaini was being marked well. Victor Anichebe did not let himself down up front, scoring one and setting up another. His performance can only enhance his chances of retaining a place in the starting lineup. Fellaini ended up with two goals, which is a measure of the player that he has become at Goodison Park, as he by no means had his best game. David Moyes's men scrapped until the final whistle and managed to salvage a point, which at least shows character.
7/10. The Villans will be heartbroken to leave with just one point. For 70 minutes, they were by far the better team. Villa were a threat on the counter all afternoon, with Charles N'Zogbia, Christian Benteke, Andreas Weimann and Gabriel Agbonlahor causing plenty of problems for the Blues. Ultimately, it was poor defending from Leighton Baines's late corner that allowed Fellaini to score; another goal from a set piece that will haunt Paul Lambert.
Mike Jones got most decisions right today. Leon Osman might have been lucky not to see stronger action taken against him late on, but his challenge on Joe Bennett looked clumsy rather than malicious.
Sports Mole's man of the match
Christian Benteke: He could be the man that keeps Villa up this season. He scored two goals and was a threat any time they went forward.
Biggest gaffe: Andreas Weimann had a glorious opportunity to put Villa 3-1 up early in the second half. He only had Tim Howard to beat after being slipped through by N'Zogbia, but he blazed well over the bar.
Everton: David Moyes takes his team to Old Trafford next Sunday to play Manchester United.
Aston Villa: The Villans play host to West Ham United in their next Premier League fixture, also next Sunday.