A tantalising battle in terrible South Coast conditions saw Dominik Szoboszlai draw first blood thanks to an all-too familiar Saints error, but Liverpool were uncharacteristically lethargic and soon fell behind to Adam Armstrong and Mateus Fernandes's efforts.
However, who else but Mohamed Salah would save Liverpool's bacon, as the 32-year-old conjured up a brilliant brace to reach 100 away goals for the Reds and propel the Merseyside giants eight points clear of Manchester City at the summit of the table.
Refusing to shy away from their high-risk approach despite the calibre of opposition, Southampton tried to play out from the back at every opportunity, but it took just one mishap for Arne Slot's side to strike first through a Szoboszlai curler.
Liverpool failed to make the most of further opportunities in the Southampton third, though, and the Reds were also in a giving mood at St Mary's, conceding a contentious penalty when Andy Robertson brought down Tyler Dibling on the edge of the area.
The VAR room determined that the challenge was made just inside the box, and even though Armstrong's spot kick was kept out by Caoimhin Kelleher, the Englishman followed up to draw the revived hosts level near the end of the first half.
Any attempt at a wake-up call from Slot at half time appeared to fall on deaf ears, as Liverpool were caught cold on the counter-attack at the start of the second half, where 20-year-old starlet Fernandes finished off a sensational back-to-front move to turn the South Coast side.
The Portuguese's strike was seemingly the rude awakening that the visitors needed, as the inevitable Salah benefitted from some more questionable goalkeeping from McCarthy to draw the visitors level, before doing what he does best from the penalty spot to complete a sensational late turnaround.
While the Reds have once again taken advantage of another Manchester City slip-up, Russell Martin's Southampton remain at the foot of the division with just four points to their name and are five adrift of safety with almost a third of the season gone.
SOUTHAMPTON VS. LIVERPOOL HIGHLIGHTS
Dominik Szoboszlai goal vs. Southampton (30th min, Southampton 0-1 Liverpool)
A Liverpool goal entirely of Southampton's making. The Saints stick to their principles and try to play out from the back, but the Liverpool press is relentless, and Flynn Downes's pass from the byline falls to the feet of Szoboszlai.
The Hungarian has all the time and space in the world to pick his spot and bends one in off the far post from the edge of the area; a mess from the Saints, but Slot's side will not care.
That goal all came about from Alex McCarthy's inexplicable decision to roll the ball out to an under-pressure Fernandes, who was never going to hold onto the ball with numerous Reds players around him.
Adam Armstrong goal vs. Liverpool (42nd min, Southampton 1-1 Liverpool)
Both sets of defences are handing out early Christmas presents at St Mary's! Virgil van Dijk and Robertson are the guilty parties this time; the former loses possession with a terrible attempt at a backheel pass, and Robertson scythes down a charging Dibling right on the edge of the box.
Referee Sam Barratt points to the spot after a brief delay, and Michael Oliver on VAR sees no reason to overturn the on-field decision.
Armstrong steps up and sees a poor spot kick kept out by Kelleher, but the rebounds falls kindly for the Saints striker to immediately make amends.
Mateus Fernandes goal vs. Liverpool (56th min, Southampton 2-1 Liverpool)
How to counter-attack 101! McCarthy claims a Liverpool corner and releases Ryan Fraser, whose deft ball over the top finds the talented Dibling on the right-hand side.
The teenager sprays a delightful cross-field pass to Armstrong, who has to check back but quickly picks out the run of Fernandes, and the 20-year-old leaves Kelleher flat-footed with a crisp first-time finish into the bottom corner!
Mohamed Salah goal vs. Southampton (65th min, Southampton 2-2 Liverpool)
One of the more unorthodox finishes from Liverpool's wing wizard, but they all count, and the Reds peg their hosts back just nine minutes after falling behind!
Ryan Gravenberch picks out the Egyptian's run with a wonderful ball over the top, and with McCarthy charging off his line, Salah nonchalantly prods the ball past him with his studs and sees his intelligent finish trickle into an open goal.
Mohamed Salah goal vs. Southampton (83rd min, Southampton 2-3 Liverpool)
When the going gets tough, Mohamed Salah.
Barratt points to the spot for the second time today, as the Egypt international's inswinging cross from the right bounces once before hitting Yukinari Sugawara on the chest and hand - stonewall.
Salah assumes the responsibility from 12 yards and picks out the side of the net with aplomb; McCarthy goes the right way, but the Liverpool winger's penalty is the definition of perfection.
MAN OF THE MATCH - MOHAMED SALAH
Special mentions undoubtedly go to Saints attacker Armstrong and the ever-graceful Gravenberch, but there was no denying Salah his rightful prize after another scintillating display that warrants a lucrative contract extension.
If he meant his first finish - which he more than likely did - it was a touch of genius, and his late pressure penalty could not have been more perfectly-placed if he tried.
SOUTHAMPTON VS. LIVERPOOL MATCH STATS
Possession: Southampton 38%-62% Liverpool
Shots: Southampton 7-27 Liverpool
Shots on target: Southampton 5-11 Liverpool
Corners: Southampton 3-10 Liverpool
Fouls: Southampton 10-9 Liverpool
BEST STATS
WHAT NEXT?
A pair of blockbuster battles are on the Liverpool menu next week, as the Reds host Real Madrid in the Champions League on Wednesday before welcoming Manchester City to Anfield for a mouthwatering Premier League showdown on Sunday.
As for Southampton, the Saints travel across the South Coast for the next edition of Friday night football, when they clash with Brighton & Hove Albion at the Amex in their next top-flight game.