Former Blackburn Rovers forward Armstrong had not scored since his debut on the opening game of the season but ended his drought in a powerful strike in the third minute.
A lacklustre Villa were fortunate not to be further behind before halftime as Southampton wasted some good chances and although they improved after the break Dean Smith's side did not do enough to merit a point.
Southampton's third win in four league games moved them up to 12th place with 14 points from 11 games while Villa are 15th, only three points ahead of third-from-bottom Burnley.
Since winning at Manchester United in late September, Villa's season has hit the buffers and they are now on their longest losing streak in the top flight since 2016.
There is nothing to suggest that they will threaten that run of 11 successive defeats, but Smith will need to address what is going wrong during the forthcoming international break.
For Southampton, who failed to win any of their opening seven games, the trajectory continues upwards.
"A very solid platform after a bad start," Southampton boss Ralph Hasenhuttl said after his side's fifth clean sheet this season.
"Last season we conceded so many goals so the biggest challenge was to get more stable defensively and we have shown we have turned things around now."
On a chilly night by the south coast, they began on the front foot on Friday and went ahead in spectacular fashion.
Villa's Matt Cash failed to deal with a high ball and Armstrong showed no hesitation to rifle a rising left-foot drive past Emiliano Martinez into the top corner.
His namesake Stuart should have doubled Southampton's lead shortly afterwards when a corner arrived to him at the far post but he screwed his shot over the bar.
Martinez then made a flying save to deny Saints skipper James Ward-Prowse as the hosts dominated.
Villa could have been down to 10 men when Anwar el Ghazi, who had already been booked, got away with a blatant dive.
The visitors were better after the break, albeit from a low base, and El Ghazi and Emiliano Buendia both went close before Villa thought they should have been awarded a penalty when Oriol Romeu clearly grabbed the shirt of Tyrone Mings.
Villa pressed late on and were handed seven minutes of stoppage time to try and salvage a point but it was not to be.
"When you are getting a run of results you get kicked in the teeth and they scored a hell of a goal," Smith said.
"I said to the players at halftime, you can't feel the world is against you and have to go and leave everything out there which is what they did. You saw what we are about in the second half, a fair score would have been a draw."