The England international converted from close range just before the hour on Monday (Tuesday AEST) as the defending Premier League champions made it two wins from two in the new campaign.
This was far from a vintage display, but the Gunners ground out the win in familiar fashion.
It was a second successive loss for Aston Villa, who are in a period of transition following a tumultuous summer which has seen a host of big-name players sold, including Ezri Konsa who received a mixed reception on his Villa Park return.
There have been arrivals as well, with striker Nicolas Jackson making his debut, and despite the loss there were positive signs.
It could have been a different story had Emiliano Buendia's effort gone in instead of crashing into the crossbar, while they could not force a leveller despite late pressure.
Inside the opening 15 minutes, Villa captain John McGinn curled an effort over before Buendia went closer from a similar range as his 22-yard effort thundered into the crossbar.
The opening 45 minutes ended without a shot on target after Ian Maatsen had drifted an effort wide after cutting in from the left.
Left-back Maatsen drilled another shot wide as Villa started the second half on the front foot.
But the game swung again and Arsenal thought they had been awarded a penalty in the 54th minute when Maatsen bundled over Saka, with Australian referee Jarred Gillett pointing to the spot after careful deliberation.
However, VAR showed the referee got it wrong as the contact occurred outside the box.
Martin Odegaard whipped the free kick just wide, but the Gunners had the momentum.
And they took the lead two minutes later.
Halftime substitute Eberechi Eze fed Riccardo Calafiori, and his ball across goal was turned in from close range by a gleeful Saka.
Villa had lost their way, but regained it as they pushed for a leveller.
Debutant Jackson played in McGinn, but the Scotland international could not sort his feet out and missed the chance to shoot, with Matty Cash's follow-up effort blocked.
The hosts thought they should have had a penalty soon after when Maatsen went down in the box, but Gillett said no and VAR did not intervene.
With men committed forward, Villa were susceptible to the counter attack and Havertz drilled an effort at straight at debutant home goalkeeper Zion Suzuki.
Villa threw bodies forward, but Mikel Arteta's side showed all the nous and game management required to see out the win as the home side ended the match without a shot on target.
15°C