Arsene Wenger's side had slipped down to third after title rivals Chelsea and then Manchester City took turns at the top over the weekend.
But Arsenal reclaimed pole position, moving one point clear of second placed City, thanks to a quick-fire double at Villa Park.
And the Gunners struck again less than one minute later when France striker Olivier Giroud showed great technique to control Wilshere's pass and fire past Villa goalkeeper Brad Guzan for his 12th goal of the season.
Christian Benteke reduced the deficit with a diving header in the 76th minute, but the Villa striker's first goal since September came too late to spark a fightback from the hosts.
A bad night for Villa was capped by an injury to Nathan Baker that saw the young defender taken to hospital with a mild concussion after being stretchered off wearing an oxygen mask.