Bukayo Saka settled a tight contest just before the hour mark, bundling home from close range in the 59th minute after a slick passing move released him inside the six-yard box. It continued Arsenal's perfect start to the title defence and avenged last season's defeat at the same ground.
Aston Villa had the better of the early exchanges without troubling David Raya, Emiliano Buendía's first-half effort cannoning back off the crossbar the closest either side came before the break.
Arsenal grew into the game after the interval, with Martin Ødegaard hitting the side netting from a free-kick after Saka was initially awarded, then controversially overturned, a penalty. Saka's goal followed minutes later, and Villa's response — including a shout for a penalty of their own — went unrewarded.
Mikel Arteta was satisfied with how his side ground out the result at a venue that beat them last season.
"Really happy, it's a massive win. It's a tough place to come and earn three points. I think we deserved it," the head coach told Sky Sports. "We had a great performance. With 11, it wasn't enough, the finishers came in and did a magnificent job to finish the game and win it.
"I know how tough it is to win here. Every big team has struggled against them because they are so good."
Substitutes Eberechi Eze and Ezri Konsa, the latter facing his former club having left Villa Park for Arsenal earlier this summer, both played a part in the winning move.
"Ebs creates the action that wins us the game. Ezri, as well, really composed and really calm with every decision he made. I'm really happy with all of them," Arteta said.
Saka, whose goal made it back-to-back wins to start the season, praised the way Arsenal adapted to a stubborn Villa defence.
"Very, very tough game. It's not easy coming here, they made it hard for us," he told Sky Sports. "The way they defend, really compact and with a high line, they caught us offside. We had to adapt to that. ... One goal is normally enough for us because we are so solid at the back. When we got the first one, it actually opened the game up. ... We weren't at our highest level with the ball. Without it, we were incredible. As soon as we lost it, we were running back."
For Aston Villa, it was a second defeat in as many league games, though Unai Emery took encouragement from the performance.
"We performed like we planned and we competed like we planned. We didn't achieve the result, of course, it's painful. ... The debut of some players was fantastic," he told Match of the Day, with Zion Suzuki and Nicolas Jackson both making their first appearances following deadline-day arrivals, while Villa also progressed talks to sign Southampton's Taylor Harwood-Bellis, who watched on from the stands.