Paul Lambert was forced to watch a dogged display from his side from the stands, as he served a touchline ban, but he will have been pleased with the ease in which Villa were able to contain the Gunners.
He also saw substitute Brett Holman come within inches of snatching a much-needed three-point haul, with the Australian midfielder seeing a 25-yard drive touched onto the crossbar by Wojciech Szczesny.
Arsene Wenger, meanwhile, will have been disappointed with Arsenal's inability to carve open a struggling opponent, with Laurent Koscielny and Aaron Ramsey wasting the best of the opportunities created by the visitors.
The Gunners have now taken only one point from their past three away games and would have fancied their chances of winning at a ground where they have been unbeaten since 1998. But they looked like unlocking Villa only spasmodically despite the runs forward of midfielder Ramsey.
Arsenal keeper Szczesny made the first save of the game in turning aside a shot from a narrow angle by Andreas Weimann before he dealt more comfortably with a long-range attempt from Barry Bannan and Christian Benteke headed wide from an Ashley Westwood corner.
Home keeper Brad Guzan made his first meaningful save after 29 minutes and the United States international reacted sharply to keep out a deflected shot from Ramsey.
Szczesny was fortunate to escape without even a yellow card when he caught the ball but then slid out of the box under pressure from Gabriel Agbonlahor. Andreas Weimann had the ball in the net after Ciaran Clark's shot from the resulting free-kick by Bannan dropped into his path but he had strayed offside.
Per Mertesacker produced a fine tackle to halt Agbonlahor's run as over-optimistic Villa fans appealed for a penalty.
Laurent Koscielny missed the best chance of the first half after 43 minutes. Olivier Giroud supplied the low cross and Koscielny found himself unmarked after a slip by Clark but he miscued his shot over the bar.
But Villa were still posing a threat to their opponents and Benteke had a header deflected past the post from Bannan's corner.
Szczesny came to Arsenal's rescue when he finger-tipped a fierce Holman effort onto the bar with 12 minutes remaining, while the visitors rarely looked like finding a winner.