The Spaniard gave the Gunners the lead after five minutes, but his opener was cancelled out when Andreas Weimann levelled the score for Villa just 20 minutes from time.
However, Cazorla struck again late on in the match to restore the hosts' lead and give them all three points.
But was it a fair result? Sports Mole gives you the analysis from the match.
On target 7
On target 3
Was the result fair?
Just about. While Arsenal were poor in parts of the match, they definitely did not deserve to lose the game. Villa were always a threat on the break and it showed with their equaliser. There could have, and probably should have, been more goals from both sides in this match, but in the end the best team just about won.
It did not take a genius to tell that Arsenal were still a bit nervy having lost their last two games in a row and being in the middle of a 'crisis', but they showed the good, the bad and the ugly of their game this afternoon. At times their football was breathtaking, with their link-up play superb. However, their poor defending and missed chances came so close to costing them, but they just came out on top.
Aston Villa's performance
Villa were so close to earning a priceless point here, and had they had held on, I would be praising the tactics of Paul Lambert. Villa largely held men back and played defensively before exposing the Gunners on the counter-attack with piercing pace. They should have scored more but could have easily conceded more as well. They can take heart and confidence from this display, but sadly for them, no points.
Sports Mole's man of the match
Santi Cazorla: Only one man can claim this award. Cazorla was brilliant for Arsenal, and in the end scored the decisive goals to earn his side the win. However, Carl Jenkinson and Jack Wilshere were both also immense for the home side.
While both sides should have done better in front of goal, mainly Olivier Giroud and Ciaran Clark, Arsenal keeper Wojciech Szczesny scoops this award. The Polish stopper should have kept out Villa's equaliser, but instead let it somehow slip through him, despite getting his hands to the ball.
Not too much for Martin Atkinson to do in this match apart from award Arsenal a huge amount of corners. He handed out a few yellow cards that were justified, but other than that, did not have too many difficult decisions to make.
Arsenal: The Gunners travel to White Hart Lane next weekend to face North London rivals Tottenham Hotspur in a huge clash, with both teams competing for a spot in the Champions League.
Aston Villa: Villa have the delightful task of entertaining the Premier League champions Manchester City at Villa Park a week on Monday.