Trailing to goals from Shane Long and Mane, fourth-placed Man City had a lifeline before the interval when Kelechi Iheanacho headed home from close range. Southampton scored a third just before the hour through Mane, however, and the Senegal international completed his hat-trick in the 68th minute.
Iheanacho scored his second for Manuel Pellegrini's side 12 minutes from time, but the damage had already been done as Man City prepare to travel to the Bernabeu next week off the back of a disappointing performance.
Vincent Kompany and Kevin De Bruyne were both left out of the Man City squad altogether, while the likes of Sergio Aguero, Fernando and Jesus Navas dropped to the bench as Pellegrini made eight changes to his XI from the goalless draw against Real Madrid in the Champions League.
As for Southampton, Ronald Koeman recalled in-form Mane, in addition to right-back Cuco Martina and midfielder Jordy Clasie in a side that showed three changes from last weekend's 4-2 win at basement side Aston Villa.
It was the home side that made the brighter start to proceedings and the first strike on goal came from the Saints in the second minute, but Joe Hart, on his 300th Premier League appearance, was down to keep out Mane's effort.
Man City did manage to settle after a fast start from the home side, but Mane sent a low strike just wide of Hart's post in the 11th minute after a sloppy piece of work from Fernandinho in the middle of the park.
Long continued to threaten with his pace in the final third and the Republic of Ireland international came close to meeting a Dusan Tadic cross in the 17th minute, before Jose Fonte headed wide of the post from a corner.
Moments later, Long again came close after releasing a strike early from a wide position, before Raheem Sterling fired straight at Southampton goalkeeper Fraser Forster after good work from Iheanacho.
Man City just could not deal with the pace of Long, however, and it was the 29-year-old that made the breakthrough in the 25th minute when he poked a Tadic cut-back past Hart after beating Nicolas Otamendi to the ball.
Southampton were not content with sitting back after opening the scoring, however, and made it 2-0 in the 28th minute when Tadic released Mane and the Senegal international fired the ball past Hart from inside the box.
Man City's half was summed up in the 35th minute when Fabian Delph sent a weak effort into the arms of Forster when the England international had better options in wide positions.
It did appear that Southampton would enter the break with their two-goal lead intact, but the visitors hit back in the 44th minute when Iheanacho headed home from close range after Martina had failed to clear inside his own box.
Iheanacho remained Man City's biggest threat and after wriggling his way into the Southampton box in the 50th minute, the striker fired low towards the centre of the goal, but Forster was on hand to make the save.
Man City continued to grow in confidence as the match approached its hour mark, but they conceded a third goal in the 57th minute when Mane converted from close range after Virgil van Dijk had rattled the crossbar with a header.
Van Dijk came close himself 25 minutes from time after producing an over-head kick inside the box, but Hart was on hand to make the save. Hart could do nothing moments later, however, as another threaded pass from Tadic found Mane, who slotted the ball into the bottom corner to complete his hat-trick.
Iheanacho was not finished for the visitors, however, and scored his second of the match 12 minutes from time when he curled an effort into the far corner to notch his 13th of the season.
Man City pressed forward in the latter stages in a bid to set up a grandstand finish, but Southampton used the ball well in the final minutes to ensure that they would win 4-2 in the Premier League for the second week in succession.
Southampton have moved above Liverpool into seventh position, while Man City remain fourth, but are just four points clear of fifth-placed Manchester United, who have a game in hand.