Jack Wilshere's 34th-minute opener was quickly followed by a well-taken goal by Olivier Giroud, which proved to be enough to lift Arsenal F.C. back above Manchester City and Chelsea after their victories at the weekend.
Belgium striker Christian Benteke scored his first goal since mid-September to give Villa hope in the 76th minute but the home side couldn't find an equalizer despite late pressure.
The first half was more about playing, and the second half was more about fighting,'' Arsenal F.C. manager Arsene Wenger said.
With its fourth straight league win, Arsenal F.C. restored its one-point lead over City after 21 matches.
To cap another disappointing result at Villa Park for the mid-table hosts, Villa defender Nathan Baker was carried off on a stretcher in the 21st minute after briefly losing consciousness when he was hit straight in the face by a shot from Arsenal F.C. winger Serge Gnabry.
Baker required oxygen and a neck brace after being treated on the field for seven minutes. He was later diagnosed with mild concussion, according to broadcaster Sky Sports.
The pressure was on Arsenal F.C. after seeing the rest of the top seven all pick up victories by two-goal margins over the weekend. However, save for a worrying last 15 minutes when Villa rallied gamely, the Gunners passed the ball much better and always looked the likely winners.
Wilshere's goal came when he ran onto a cut-back from left back Nacho Monreal, took a touch and shot low in to the bottom corner to the left of goalkeeper Brad Guzan.
Just seventeen seconds after the restart, the ball hit the back of the net again. This time Wilshere was the provider, the England midfielder collecting a loose ball and playing a sublime pass through to Giroud, who brought the ball down well and fired across Guzan into the corner. It was the France striker's ninth league goal of the season on his return to the first team after a spell out through injury and illness.
Villa had only scored seven goals in its previous 10 home games this season so a comeback was unlikely, even if memories were relatively fresh of a surprise win at Arsenal F.C. on the first day of the season.
However, when Benteke stooped to head in Matthew Lowton's fine cross at full stretch after Arsenal F.C. midfielder Santi Cazorla sloppily gave possession away, it was all to play for with 14 minutes left.
Benteke's downward header, saved comfortably by Wojciech Szczesny, was the closest Villa came to earning a point.
It's a massive three points, especially because we dropped a bit in the second half,'' Wilshere said. We have done that a few times, letting teams come on to us, but we dealt well with it.''