Captain John McGinn gave Unai Emery's side the lead after just seven minutes, when he controlled a cross from Leon Bailey and blasted a shot past David Raya.
Villa survived a sustained spell of pressure from Arsenal late in the game and the Gunners also had a late Kai Havertz effort ruled out for handball following a lengthy VAR review.
The Villans held on for a 15th consecutive Premier League win under Emery across last season and this one and are two points behind leaders Liverpool with 16 games played.
Emery's side have now beaten three of the top six in the past two weeks, having defeated Tottenham in north London in late November, before a win against Manchester City in midweek and Saturday's victory against Arsenal.
In between the win at Spurs and the victory against City, Villa drew 2-2 against Bournemouth.
After the win against his former club Arsenal, Emery was not getting carried away.
Asked about the title, he said: "I will speak when we are in [week] 30, 32, and if we are in the same position then as we are now, I can speak about [the title race]."
And speaking on Sky Sports, McGinn joked: "I'm banning the T-word. It's game week 16, so there's a long, long way to go, and we respect everyone in front of us who have been in this position for years.
"We're newbies. Can we keep it up? Hopefully."
More Aston Villa stories
Aston Villa goalkeeper says Argentina team-mate Lionel Messi is "the only player in history to complete football" and has revealed his pre-match meal ahead of last year's World Cup final.
Meanwhile, Villa have been linked with a January move for Real Madrid midfielder Dani Ceballos.
And in-form striker Ollie Watkins is set for talks over a new contract at Aston Villa amid links with Arsenal, the club he supported as a boy.
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