Alisson Becker earned deserved plaudits and remained, for the most part, Liverpool's rock in some disconcerting passages of play.
A nervy second half was bookended by Thiago Alcantara's first goal in Red, assuring three points stayed at Anfield and top four hopes remained in tact.
Here is the Warm Down as the Reds kept their European dream alive for another gameweek at least.
It would be no underestimation to say hopes of a top four finish would have been dashed but for the imperious display from the Brazilian between the sticks.
Alisson recorded six saves on the night, the most in a game in the Premier League era for Liverpool, with a 100% success rate in duels to boot according to FBref.com.
The clean sheet put an end to Liverpool's recent run of conceding at least once in each of their last eight Premier League home games.
The number one made his presence count on numerous occasions, going against the grain and help carry his side through faltering periods in a match that seemed destined for a Southampton goal.
This was epitomised none more so than when Sadio Mane put away Liverpool's first goal, where 46 seconds earlier a vital double stop from the 'keeper prevented both Che Adams and Nathan Redmond from breaking the deadlock before the ball made its way up the pitch.
Michael Obafemi's introduction prompted Alisson out from his 18-yard area to play the sweeper role, with Rhys Williams, who made his first start since a loss against Fulham on 7 March, was found wanting after being caught out by the Irishman's pace.
With the lead at just one, the 'keeper was momentarily possessed by the lapses in concentration shown by his peers recently, executing a stray pass to Adams but bailed himself out of trouble after recovering a tame effort from the striker.
An imperfect performance symptomatic of an imperfect season for Liverpool.
The aforementioned opening goals was one of firsts for Mane and the Reds.
It was the left winger's first in nine games and first at Anfield in the calendar year, concluding an uncharacteristic dry spell for the Senegalese, who is still yet to reach the double figure goal-haul that he has notched in each of his Premier League seasons (currently on 9 Premier League goals).
Mane had a good chance to score earlier on after meeting a whipped Trent Alexander-Arnold ball at the base of the penalty box, directing a shot high and wide after pressure from Jannik Vestergaard.
It was Mo Salah who set up the goal with an almost equally sumptuous ball to the far post, the first time Salah assisted his striking counterpart in the league this season with Mane nodding home.
The stat is a stark reminder that despite Liverpool's defensive absentees (5 centre-backs were on Liverpool's injury list going into the match), their woes are just as endemic in the front line in what has become an outlandish campaign for the Anfield outfit.
Thiago Alcantara's first 90 minutes typically went under the radar, whose arrival on Merseyside has hardly lived up to the lofty expectations bestowed upon the 30-year-old adapting at Liverpool.
The midfielder won half of his duels, made the second most tackles for his team on the night and stayed out of the referees book, something that has been rightfully been called into question since pulling on the Red shirt.
The most impressive feature of his game was his passing and range of distribution, with an impressive stat line consisting of a 93% passing success rate (the best in the game) with an accompanying nine successful long passes from 11 attempted according to FBref.com.
It wasn't until the 91st minute when his presence commanded the attention of all viewers, as his goal, his first for the Redmen, wrapped up the result for his side.
The goal was a monkey off his back and was unequivocally deserved, swept into the far corner with the nonchalance utilised for his pinpoint lofted passes after receiving a layoff from substitute Roberto Firmino.
From topping the table back in November, the inconceivable thought of being ten points adrift of the drop has been quite the fall for the reputable Ralph Hasenhuttl and his Southampton side.
No side has accumulated less points (11) and conceded more goals (42) thus far in 2021, but nonetheless they arrived into the game in hope of picking up a historic league double over Liverpool for just the third time in their history, having beat the Reds in the new year courtesy of a Danny Ings goal.
The Saints were boosted by the availability of Jannik Vestergaard after his red card against Leicester was rescinded, but were without Ings against his former club, along with a plethora of other stars like loanee Takumi Minamino (ineligible to play against his parent club).
Few on the pitch stood up to take advantage of opportunities that were frankly at times presented to them, notably Che Adams but also the likes of Ibrahima Diallo, whose venemous volley hardly troubled Alisson in the second half.
Nathan Tella, the young winger whose link up play impressed in the first period, was also unable to glance a Nathan Redmond cross either side of a resolute Alisson.
In the hunt for Europe
"I'm not sure there is still a chance but we'll try to make sure that if there is one, we will be there."
Ever the realist, that was the statement from Jurgen Klopp in his pre-match press conference ahead of Saturday's crucial game.
Coming into the game the players would have received a big boost as Leicester and Tottenham dropped points, but a late win for Chelsea at the Etihad only served as more impetus for a win at Anfield.
Now with a game in hand over Leicester, a six point gap seems more attainable and not necessarily an insurmountable task, but European away days next year in Europe's biggest club competition are dependent on results of other sides.
Particularly given Leicester face an unenviable run-in of Manchester United, Chelsea and Tottenham, Klopp and co. will be cautiously optimistic as they face four more cup finals of their own.
The battle isn't over just yet.