Dean Smith's side did not muster a single shot on target in a dismal display which will set more alarm bells ringing in the west midlands.
Long's eighth-minute strike and Armstrong's stoppage-time break-away, after Pepe Reina had gone up for a corner, eased a Saints side who not so long ago looked relegation-bound themselves to the relative safety of 34 points.
Villa, however, remain just a point above the drop zone and could well be back in it after the weekend.
Southampton kicked off with the worst home record in the Premier League but it did not show as they tore into a Villa side with woeful form on the road.
They were inches from taking the lead when young defender Will Smallbone collected Moussa Djenepo's pass on the edge of the box.
Smallbone's shot took a deflection off Tyrone Mings to wrong-foot Villa keeper Reina, who was relieved to see it clip the outside of his post.
But moments later the hosts took the lead, Djenepo reaching the byline and cutting the ball back for Long to bundle in at the near post.
Long can hardly be described as a prolific goalscorer unless, it seems, he is playing Villa. This was his seventh goal in his last seven appearances against them.
Danny Ings, by contrast, has been lethal in front of goal this season but when he went through one-on-one with Reina he put his shot too close to the Spaniard.
On a blustery day on the south coast Villa were in danger of being blown away, but Reina did well to save from Djenepo after he was teed up by Ings.
A couple of lengthy injury delays briefly took the wind out of Southampton's sails and Villa had the ball in the net shortly before half-time, although Mbwana Samatta had been flagged offside before he converted Jack Grealish's pass.
Reina saved a fierce volley from Pierre-Emile Hojbjerg before taking one for the team when he was booked for shoving Long outside the area following a poor attempt at a header.
As for Villa, the closest they came to forcing an equaliser was substitute Trezeguet's effort which fizzed across goal and wide.
Their misery was compounded in stoppage time when Armstrong rolled the ball into an empty net from 35 yards after Reina had long since given up the chase.