Going into the game tied on points in the table, Liverpool outclassed their hosts in the first half and were deservedly two goals to the good at the break, having been lucky to escape conceding an early penalty.
Philippe Coutinho and Daniel Sturridge scored within five minutes of one another as Liverpool dominated the first half but Mane, available after seeing his red card against Stoke rescinded, hit a brace either side of a fine Graziano Pelle strike to seal a memorable 3-2 win for Ronald Koeman's side.
Mane could have had an instant impact but missed a 49th-minute penalty, only to then become the hero of the piece as Jurgen Klopp saw Liverpool lose for the first time in nine.
Southampton had started well and had strong calls for a penalty turned down by referee Roger East as Shane Long turned former Saints defender Dejan Lovren before bursting into the box and went down in the box as the Croatian looked to close him down.
Pelle then fired over from Steven Davis' pass before Liverpool started to create chances, Sturridge stinging the palms of Fraser Forster before accidentally blocking Divock Origi's strike.
But no-one could get in the way of Coutinho's opening goal just seconds later as the Brazil international curled a shot past Forster from 25 yards with 17 minutes on the clock.
Liverpool won here 6-1 in the Capital One Cup back in December and for large periods of the first half they threatened to run riot once again.
They were soon two ahead as a lightening counter-attack left Origi and Sturridge against two Saints' defenders - and it was the latter who tucked away Liverpool's second having been picked out by Origi.
Joe Allen should have added to Koeman's woes as he burst into the box but his shot was too close to Forster, who kept the effort out with his foot.
Southampton could not get themselves together at the back and, after Jordy Clasie surrendered possession, they were lucky Liverpool wasted a three-on-two counter-attack which ended with Sturridge shooting tamely at Forster.
Coutinho drifted in a corner just after the half-hour mark and, as it dropped to Allen, the Wales international finished into the corner but his celebrations were short-lived as Mamadou Sakho was deemed to be interfering with play while stood in an offside position.
Koeman reacted at the interval, making a double change as Mane and Victor Wanyama replaced Dusan Tadic and Clasie - while Martin Skrtel came on in place of Lovren for the visitors.
Two of those substitutes were involved immediately, Skrtel conceding a penalty as he tugged down Pelle, with Mane stepping up only to see his tame spot-kick pushed out my Simon Mignolet.
Mane and Oriol Romeu both came close before the former made up for his earlier penalty miss by turning Sakho in the box and firing home.
And, with the pressure continuing to build on Liverpool's back-four, Pelle thrashed home his third goal in two games (83) to bring the game level before setting Mane away to convert the 86th-minute winner as Saints go seventh.
TWEET OF THE MATCH
"Get in!!!!!!!!!! (whilst watching Kung fu panda 3)"
Matt Le Tissier @mattletiss7
Fraser Forster: 6 (out of 10)
Cuco Martina: 5
Virgil van Dijk: 5
Jose Fonte: 5
Ryan Bertrand: 6
Oriol Romeu: 6
Jordy Clasie: 5
Shane Long: 6
Steven Davis: 7
Duan Tadic: 5
Graziano Pelle: 8
Sadio Mane (for Tadic, 45): 8
Victor Wanyama (for Clasie, 45): 6
James Ward-Prowse (for Romeu, 69): 6
Simon Mignolet: 7
Jon Flanagan: 6
Dejan Lovren: 5
Mamdou Sakho: 6
Nathaniel Clyne: 6
Emre Can: 7
Joe Allen: 7
Adam Lallana: 7
Philippe Coutinho: 7
Divock Origi: 7
Daniel Sturridge: 7
Martin Skrtel (for Lovren, 45): 5
Christian Benteke (for Sturridge, 69): 5
Sheyi Ojo (for Allen, 87): 5
Graziano Pelle: Mane may have scored two, but Pelle's work-rate was second to none
He thrashed Saints level with a tremendous strike and was involved in the winner having been dragged down for the second-half penalty, too.
MOMENT OF THE MATCH
Sadio Mane: With Liverpool reeling, Mane secured a spectacular comeback victory with a cool, controlled finish past Mignolet - more than making up for his poor penalty at the start of the second half.
VIEW FROM THE BENCH
Klopp will wonder how his side managed to lose a game from such a strong position but it was Koeman who was dancing down the touchline as Southampton bounced back
The Dutchman made two changes at half-time after a shoddy first 45 minutes and, with Mane in particular, his decision was inspired.
MOAN OF THE MATCH
Not much to complain about following a five-goal thriller but Roger East's decision not to award Southampton an early penalty could have cost Saints dear were it not for their spirited comeback
The referee seemed very keen to point to the spot early in the second half - but Southampton conspired to miss that one anyway.
WHO'S UP NEXT?
Leicester v Southampton (Sunday 3 April)
Liverpool v Tottenham (Saturday 2 April)
Source : PA