The hosting Gunners started the brighter of the two sides and went close to breaking the deadlock through Jack Wilshere with just two minutes on the clock. The midfielder cut in from the left, but Villa goalkeeper Brad Guzan was equal to his curling effort.
However, just one minute later Arsenal were in front. Cazorla saw his initial shot blocked, but his second effort from inside the area beat Guzan, who managed to get a weak hand to the ball.
Despite having fallen behind, Villa rallied and went close to levelling up proceedings on two occasions.
First Gabriel Agbonlahor saw his low shot parried clear by Wojciech Szczesny with 10 minutes played and then 15 minutes later the Arsenal goalkeeper was on hand to deny Charles N'Zogbia's effort from inside the area.
As the half drew to a close both Theo Walcott and Olivier Giroud had chances to double Arsenal's advantage, but the England international fired over while the latter saw his strike from the left of the target saved by Guzan.