Arsene Wenger's men had slipped to third thanks to victories for Chelsea and Manchester City over the weekend but first-half strikes from Jack Wilshere and Olivier Giroud saw Arsenal back on top, with the London club now unbeaten at Villa Park in their last 15 league visits.
Villa had held firm until two quick-fire goals handed Arsenal the initiative. First Wilshere capped a flowing move with a neat finish on 34 minutes, before he turned provider for Frenchman Giroud to side-foot past Brad Guzan a minute later.
The hosts improved somewhat after the break and were rewarded with 15 minutes remaining when Christian Benteke, who scored twice in Villa's opening-day 3-1 triumph at the Emirates, headed home his first Premier League goal since September 14.
Arsenal's winning run in the league now stretches to four matches, while Villa remain in 11th position.
Ron Vlaar and Gabriel Agbonlahor were among five players restored to Villa's starting line-up from the 2-1 FA Cup defeat to Sheffield United, while Arsenal welcomed Giroud back from an ankle problem.
The visitors made a bright start and almost went ahead as early as the fifth minute when Giroud flashed a header wide from Bacary Sagna's teasing cross.
Paul Lambert's men were dealt a blow as Nathan Baker had to exit play after 15 minutes when Serge Gnabry's shot struck him in the face, with Leandro Bacuna coming on.
Villa looked more threatening when play resumed, with Karim El Ahmadi scooping over the crossbar from Fabian Delph's centre.
But the home side's evening unravelled as Arsenal scored two goals in as many minutes.
A slick opening led to Nacho Monreal picking out Wilshere on the edge of the area and the England international moved into the area before calmly slotting home.
Wilshere was involved in the second, chipping a pass into the path of Giroud, who took one touch before steering his effort beyond Guzan.
Villa improved after the break and Bacuna should have done better when he shot straight at Wojciech Szczesny from the edge of the area.
Arsenal remained comfortable in possession, however, and Cazorla tested Guzan with a driven left-foot effort on the hour mark.
The away side came even closer on 72 minutes with a bending strike from Giroud curling just wide of the left-hand post.
Villa ensured a nervy ending by halving the arrears with quarter of an hour remaining when Benteke dived to meet Matthew Lowton's superb cross from the right-hand side and end an 11-match league run without a goal.
Wenger introduced Alex Oxlade-Chamberlain late on, marking the winger's return from the knee injury suffered on the opening day against Villa, as Arsenal held on despite late pressure.
