The 23-year-old fired three goals in two minutes and 56 seconds – eclipsing Robbie Fowler’s record of four minutes and 33 seconds – to put the hosts three up after just 16 minutes, before Shane Long tapped one in and struck a superb fifth from long-range.
Christian Benteke pulled one back to make it 5-1 at half-time, but Graziano Pelle then blasted in a sixth late in the second half as Ronald Koeman’s men enjoyed a fine afternoon with their first win in five top-flight outings.
Villa needed a win to guarantee Premier League safety ahead of the day’s other games, but Hull’s defeat at Tottenham later on Saturday confirmed their survival, as it leaves Tim Sherwood’s men four points clear of the Tigers going into the last game of the season.
It initially looked like Southampton might not be in luck as Graziano Pelle met Nathaniel Clyne’s ball from the right and fired a low first-time shot into the net, only to be wrongly flagged offside.
But on 13 minutes the Villa capitulation started as Mane latched on to Pelle’s flick before racing into the box, the ball rebounding off Shay Given before the Senegal international fired the ball into an empty net.
Just over a minute later, Ron Vlaar’s misplaced pass back to Given was intercepted by Long, who managed to win a challenge with the goalkeeper as the ball fell for Mane, who again had an open goal to fire into.
The hat-trick was then complete two minutes and 56 seconds after his first as Long charged down the left-hand side and squared it to the edge of the box, Mane firing an excellent first-time finish into the top corner to register his record treble.
It was nearly 4-0 two minutes later when Sherwood’s men couldn’t deal with another ball over the top, this time from Nathaniel Clyne, but James Ward-Prowse could only fire his shot straight at Given.
The home fans did not have to wait too long for the fourth, though, as on 26 minutes Mane slotted an excellent ball through the defence looking for Pelle, whose low effort was turned away by Given before Long was there to meet the rebound.
Villa were shellshocked, and it got even worse as Long registered his second in the 38th minute, catching Ashley Westwood in possession before spotting Given off his line and curling a stunning 40-yard strike into the net.
Benteke pulled one back in first-half stoppage time as he powered a header into the top corner from Leandro Bacuna’s cross – Villa’s 500th Premier League goal away from home – but the damage had already been done.
Southampton took their foot off the gas in the second half with the three points already secured, but Villa struggled to create anything meaningful as the Saints’ defence coped with every cross and long ball.
Substitute Maya Yoshida almost scored with his first touch after coming on, meeting Ward-Prowse’s corner with a powerful header, only to see it parried away by Given.
On 81 minutes, though, the sixth goal came as Mane turned provider, picking the ball up on the right and drilling in a low cross for Pelle, who left the hapless Jores Okore in his wake and blasted a first-time finish into the roof of the net.
Villa had a couple of chances late on as substitute Gabriel Agbonlahor fired Alan Hutton’s low ball straight at Paulo Gazzaniga, before he tested the goalkeeper with another low drive across goal, but the Southampton shot-stopper turned it away with a good save.
Southampton: Gazzaniga (7), Clyne (7), Fonte (6), Alderweireld (7), Bertrand (7), S Davis (7), Wanyama (6), Ward-Prowse (8), Mane (9), Pelle (8), Long (9).
Used subs: Yoshida (7), Djuricic (7), Elia (6).
Aston Villa: Given (4), Bacuna (5), Vlaar (4), Okore (3), Hutton (6), Westwood (5), Delph (6), Cleverley (6), N’Zogbia (4), Grealish (6), Benteke (5).
Used subs: Agbonlahor (7), Lowton (6).
Man of the match: Sadio Mane