The duo combined again for the second shortly before half time, although this time the roles were reversed as Firmino's delightful flick set up Salah to stroke the ball home.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
Huddersfield's win over Bournemouth, coupled with Tottenham's victory in the North London derby yesterday, means that this is now fourth from top against fourth from bottom, with both sides coming into this match desperate for a win which could have a big impact at both ends of the table.
We will have a close look at the situations both clubs find themselves in in a short while, but first let's have a butchers at the team news...
Well, it was always going to be all eyes on Virgil van Dijk when that team news came out, and as expected the centre-back does start for Liverpool on his first return to St Mary's since leaving last month.
Van Dijk made the move on January 1 for a world-record fee of £75m, becoming the sixth player to swap Southampton for Liverpool since June 2017, for a combined total of £172.5m. Van Dijk is likely to get a more hostile reception than most of those who preceded him, though, having pushed for a move away last summer.
Oxlade-Chamberlain returns to the starting XI for this one, but fellow former Southampton players Lovren and Lallana have to make do with a place on the bench from the start in this one. Lallana is still recovering from a thigh injury, but is fit enough to be included in the matchday squad today, despite being sent off for the Under-23s earlier this week.
Salah's brace against Spurs last time out - including a dazzling second goal - saw him become the quickest player to 20 league goals for Liverpool since 1915, and he now needs just one more left-footed goal to equal Robbie Fowler's record for the most of those in a Premier League season, which currently stands at 19.
The concern for Liverpool will be that they are overly reliant on Salah, as they have failed to win any of the five league games in which he has not provided a goal or assist this season.
Emre Can keeps his place in midfield and gets the armband this afternoon, but alongside him Wijnaldum and Oxlade-Chamberlain return to the fold, with Henderson missing out entirely and Milner dropping to the bench.
The change comes in midfield as Pierre-Emile Hojbjerg comes back into the side, replacing the slightly more attack-minded Sofiane Boufal. It is a nod to Liverpool's attacking prowess, although Hojbjerg is certainly capable of helping Southampton go forward themselves too.
Pellegrino has been forced to throw the Argentine in at the deep end to a certain extent due to injuries to Austin and Gabbiadini - the latter of whom is included on the bench despite concerns over a hip problem - but the Saints will still expected big things from their new striker.
Lemina scored a cracking goal against West Brom last weekend before Ward-Prowse later joined him on the scoresheet, and the Englishman may fancy his chances of doing more damage today. He has been in fine attacking form recently, and his set-piece deliveries could wreak havoc against a Liverpool defence who have traditionally struggled to deal with those.
Stephens has scored in three consecutive Southampton appearances, having failed to find the back of the net in his first 38 competitive outings for the club. Liverpool will need to keep an extra close eye on him up from the back this afternoon.
The Southampton board may well be rueing the decision to sack Claude Puel in search of more entertaining and attacking football last summer now, with the Saints beginning the day seven points and six places worse off than they were at the same stage of last season.
The Saints began the day in 16th and one point clear of the relegation zone, but Huddersfield upset the formbook with an impressive 4-1 triumph over Bournemouth in the day's early kickoff and Newcastle are currently on course to pull off an even bigger shock, leading Manchester United 1-0.
Huddersfield and Newcastle occupied the two places directly below Southampton at the start of today, so those scores have only cranked up the pressure heading into this match.
However, it is their Premier League form which remains unconvincing and has seen them slip closer and closer to trouble. The Saints are unbeaten in their last four top-flight outings, but three of those have been draws.
Southampton do come into this match off the back of one of those rare victories, though, coming from behind to beat West Brom 3-2 at The Hawthorns last weekend to finally end what was a 12-match winless streak in the league which stretched all the way back to November.
That is about where the parallels between that match and this match end, though, and at the very least Southampton will need to significantly improve their recent home form if they are to get anything out of this game.
Indeed, since the aforementioned visit to Everton, Southampton have taken only four points from a possible 18 here at St Mary's, while all season they have only won three home games - the second-lowest tally in the division.
Only Newcastle and West Brom have picked up fewer points in front of their own fans, and as things stand with Newcastle beating Manchester United it would only be West Brom by the time Southampton kick off here.
The Saints have, in fairness, taken points off Tottenham, Arsenal and Everton here so far this season, but they have not beaten one of the 'big six' teams in a home league games since their 4-2 triumph over Manchester City in May 2016.
At least one of Tottenham and Arsenal were guaranteed to drop points in the top-four race when they faced off in the North London derby yesterday, but Liverpool will have been hoping for a draw and, failing that, an Arsenal win. As it was, though, Tottenham's 1-0 win lifted them up to third, sending Liverpool down to fourth in the process.
Defeat for Liverpool would be a huge setback, and could result in them finishing the weekend outside the Champions League places depending on Chelsea's result when they take on West Bromwich Albion on Monday night.
The Reds have won just one of four games across all competitions since then, including two defeats having been unbeaten in 18 prior to that.
That only tells half of the story, though, with Kane having earlier missed another penalty during an action-packed final 10 minutes, and both spot kicks being hotly contested and requiring lengthy discussions between the officials. Add to that wonder goals from Wanyama and Salah in the final 10 minutes too, and it truly was a rollercoaster end to the game.
Only Man City have lost fewer matches in the top flight all season, although the shock nature of their recent defeat to Swansea should ensure that they do not take their eye off the ball for this match, with the first leg of their Champions League tie against Porto coming up on Wednesday.
The Reds have lost just one of their last nine away games across all competitions, winning six of those, and have suffered only two defeats on their travels since September.
Indeed, their current tally of 32 away goals in just 13 Premier League outings is just one short of their total for the whole of last season, and five more than they have managed in front of their own fans.
Liverpool are always a difficult one to call in these types of matches. Everything on paper points to an away win, but these are exactly the games Liverpool often slip up in. Even so, we are backing the visitors to come away with all three points this afternoon.
SPORTS MOLE SAYS: Southampton 1-3 Liverpool
One of those wins did come in the reverse fixture, though, with Salah scoring a first-half brace before Coutinho capped off the scoring in a 3-0 win, ending a five-match winless run for Liverpool against today's opponents.
However, they have not won here in the league since February 2015, with Coutinho and Sterling were the scorers in a 2-0 victory. Southampton come into this match unbeaten in their last three home fixtures against Liverpool in all competitions, most recently running out 1-0 winners in the League Cup semi-final last season.
The last two meetings between these two sides here have yielded just one goal in total, compared to 12 goals in the two before that. Let's hope for a return to the latter this afternoon!
SOUTHAMPTON STARTING XI: McCarthy; Cedric, Stephens, Hoedt, Bertrand; Romeu, Lemina, Hojbjerg, Ward-Prowse, Tadic; Carrillo
LIVERPOOL STARTING XI: Karius; Alexander-Arnold, Matip, Van Dijk, Robertson; Can, Wijnaldum, Oxlade-Chamberlain; Salah, Firmino, Mane
The hosts have looked shaky in defence already, and another error leads to this one here. Liverpool break and Wijnaldum's ball forward should be cut out by Hoedt, but he completely misses his attempted clearance. Salah then picks it up before rolling the ball into the path of Firmino, who makes no mistake with his decisive finish.
20 - Roberto Firmino has scored 20 goals in all competitions in a single season for the first time since 2013-14 with Hoffenheim (22). Clinical. pic.twitter.com/9d7SOaAeBK— OptaJoe (@OptaJoe) February 11, 2018
WATCH: Hoedt horribly misjudges a ball forward from midfield and Salah squares to Firmino, who beats McCarthy one-on-one with ease!
Follow live updates and in-game clips and watch live on Sky Sports Premier League: https://t.co/0YvjnsJTla https://t.co/teHN1aPZUH— Sky Sports PL (@SkySportsPL) February 11, 2018
Matip feeds the ball into the path of Salah, who quickly gives it to Firmino before darting into the box. Firmino waits before producing a magnificent back-heel perfectly into his path, and from there there is only ever going to be one conclusion as Salah tucks the finish home.
29 – Mohamed Salah has been directly involved in 29 @premierleague goals this season (22 goals, 7 assists); the most by a @LFC player in their debut season for the club in the competition. Heroic. pic.twitter.com/4YNjRW3Xqg— OptaJoe (@OptaJoe) February 11, 2018
Southampton were on top for most of the half and had their chances to be leading themselves going into the break, but Liverpool have been more clinical, scoring at the beginning and end of the half to put themselves in control of the game.
That gifted possession to Mohamed Salah, who in turn rolled the ball into the path of Firmino. The Brazilian never looked like missing as he tucked his finish into the bottom corner with aplomb, bringing up 20 goals for the season.
The Egyptian traded passes with Firmino, whose returned ball was a brilliant back-heel perfectly into the path of Salah, who stroked his finish past the keeper. It was another stunning piece of link-up player between the two attackers, who have been the difference so far today.
The best opened fell the way of Hojbjerg, who was thwarted from close range by Karius after being picked out by Romeu's pass. Ward-Prowse has also had two good headed chances which Karius has kept out, while Carrillo also threatened aerially for the home side.
While it was a very good day for Liverpool, it was a dreadful one for Southampton as the two teams below them in the table also won, leaving the Saints in the relegation zone and a point from safety after succumbing to first-half goals from Roberto Firmino and Mohamed Salah.
Thank you very much for joining Sports Mole for today's late kickoff as Liverpool beat Southampton to climb back up to third, leaving the Saints in the relegation zone in the process. I will leave you with our match report, and be sure to stick around for reaction from both camps too.
From me, though, it is goodbye for now!