Thomas Partey headed in Smith Rowe’s corner for his first goal for the Gunners – having earlier hit the crossbar.
Right at the end of the first half, Arsenal were given a penalty after a long video assistant referee review for a Matt Targett foul on Alexandre Lacazette.
Pierre-Emerick Aubameyang’s penalty was saved excellently by former Arsenal keeper Emiliano Martinez, but the Gabon striker put home the rebound from close range.
Villa improved on a thoroughly wretched first half, but Smith Rowe scored Arsenal’s third 11 minutes into the second half.
He won the ball in his own half and then finished the move via a deflection and the post.
The visitors got a consolation when Jacob Ramsey curled his first Villa goal into the top corner from 20 yards. They put on good pressure and created a few chances in the closing stages but it was too little, too late.
Villa saw two bids for England Under-21 international Smith Rowe turned down in the summer, with Arteta insisting he was never worried he would leave the Emirates Stadium.
Smith Rowe now has two goals and two assists this season and Arteta has been pleased with the development of the academy graduate.
He said: “When you want to take the game to the next level, when you become a real important player in such a big club, that should be the only priority and every detail is important and relevant.
“You have to make him aware of that, you cannot give percentages away that can make big differences and he has changed that.
“There is no complaining, he is just looking forwards, he is really determined, he has changed the way he is living as well a little bit and some of the habits that he had and he’s been superb.”
More like it from Arsenal
This did not look like a game between two teams sitting next to each other in the table – but Arsenal were 12th and Villa 13th before kick-off.
Arsenal are capable of good spells – like at the start of Monday’s 2-2 draw with Crystal Palace – and good games – like the 3-1 win over Tottenham.
This was one of the good games, well for 80 minutes.
Aston Villa were the opposite of their 3-2 defeat by Wolves. They collapsed there in the final 10 minutes – but this time that was when they they had most of their chances.
They did not manage a shot in the first half, the first time since May 2018 that has happened to a team playing against Arsenal in the league.
The Gunners should have been out of sight – Partey had hit the woodwork from close range before headed them into the lead.
Aubameyang had a goal disallowed for a debatable Lacazette foul and Martinez made several smart saves.
But Arsenal got the second they deserved in first-half injury time. The crowd thought Craig Pawson was whistling for half-time but he was actually stopping play for a VAR consultation.
Targett was about to clear the ball when Lacazette stepped across him and drew a foul instead. The penalty was given and Aubameyang scored at the second attempt.
Villa had more threat when they brought on winger Leon Bailey for defender Axel Tuanzebe at half-time, but after their first couple of chances, Smith Rowe wrapped it up.
Or so it looked until Ramsey scored the best goal of the game. Ollie Watkins, Ramsey and Bailey all had chances to for Villa but could not set up a tense finale.
Smith ‘confused’ about penalty
Aston Villa manager Dean Smith told BBC Sport: “First half we got dominated physically. I can take the second half. I don’t expect us to get dominated physically though. You can’t give teams in the Premier League a head start.
“We knew Arsenal would start quickly but we allowed them to control the first half.
“I am confused about the penalty. We spoke at length [before the season] about the lower-contact frivolous penalties.
“I have seen it once and can’t work out if he touches ball first or man. If we are looking at a penalty that long maybe they aren’t given.”