Jannik Vestergaard's thunderous header opened the scoring for the away side, before James Ward-Prowse superbly grabbed a brace of free-kicks on his birthday.
Danny Ings' brilliant effort into the top corner in the second half killed off any chance of a Villa comeback, before Tyrone Mings and Ollie Watkins halved the scoreline.
In the closing moments of injury time, Jack Grealish curled the ball into the front post in a spirited second-half performance by Villa.
Villa have now lost their previous two games after winning their opening four league games.
The defeat now means Villa remain winless against the Saints for eight top-flight meetings.
Story of the match
Against a defence that has only conceded five goals all season, Southampton thought they had breached a resolute Villa defence after two minutes when Ezri Konza's touch fell into the net.
However, VAR ruled out the goal after Che Adams was offside from the corner that led to the goal.
Ralph Hassenhuttl's side fast start continued and they nearly took the lead, again, when Theo Walcott clipped the top of the crossbar unmarked just outside the penalty area.
Villa grew in confidence as the game aged, with Grealish having a curled-effort deflected wide, but it was the visitor's who broke the deadlock.
Following a foul on Kyle Walker-Peters, a sensational delivery from birthday boy Ward-Prowse was powered into the roof of the goal with ease by Vestergaard.
The goal was the centre-back's second straight away goal after scoring at Chelsea two weeks ago.
Villa were forced into an early change when Bertrand Traore's first start for his new club was cut short after only 28 minutes due to injury. Trezeguet, who was dropped by Dean Smith for Traore, was brought onto the right-wing.
However, the home side's problem's went from bad to worse when Ward-Prowse doubled Southampton's lead with a brilliant free-kick past Emiliano Martinez.
After his goal last week against Everton, Ward-Prowse became the first Saints player to score in the Premier League on his birthday since Neil Maddison in 1993.
Southampton made it 3-0 on the brink of half-time through another Ward-Prowse free-kick. Adams' ball to Walcott was stopped by the hand of Matty Cash, who was lucky to only receive a yellow card, on the edge of the penalty area.
The Saints skipper stepped up and curled the ball into the back of the net to score his eighth-goal through a direct free-kick for the club, overtaking Matt Le Tissier.
With a mountain to climb, Villa came close to reducing the deficit when Trezeguet saw his header pushed away from Alex McCarthy before the keeper denies Grealish from a header.
However, Southampton claimed even more control of things when Ings' superb shot arrowed into the top corner.
The goal means Ings now has five for the season, level with Wilfried Zaha and Harry Kane, and only Jamie Vardy (29) has scored more Premier League goals than the 28-year-old since the start of last season.
A depleted Villa cancelled out Ings' strike through Mings, who headed Grealish's smart cross home.
The visitors remained solid at the back and seemed like they would only concede the single goal, until Ibrahima Diallo fouled Grealish in the penalty box, resulting in Watkins to grab his fourth goal since his move from Brentford.
Grealish's late goal meant his side only lost by one goal, but Villa's first-half performance meant there was too much to do.
Villa's zonal-marking is not working
For the opening goal of the game, Vestergaard managed to head the ball, leaving Martinez with no chance.
One of the most frustrating elements of that goal for Smith and his staff will be how it managed to happen.
The hosts' set up with zonal marking for set-pieces, with John McGinn marking Vestergaard whilst Konza and Mings were left marking a 'zone'.
Against a physical side such as Southampton, man-marking would have been better suited with the physicality of either centre-back potentially able to deny the Danish defender space.
James Ward-Prowse is a special player
The scorer of Southampton's 1,000th Premier League goal, Ward-Prowse put on display one of his best performances against Villa.
Grabbing an assist for the first goal and two sensational free-kicks, Ward-Prowse was the glue in the Saints' impressing victory.
His two goals meant he is the only player in the last five years to score two direct free-kicks in the same game since Christian Eriksen did the same against Swansea City in 2015.
The club captain was vocal in encouraging his teammates and managed to nullify any danger coming through Ross Barkley or McGinn.