The visitors took a third-minute lead through playmaker Philippe Coutinho’s brilliant long-range strike, before wrapping up the points thanks to a Raheem Sterling goal 17 minutes from time.
Victory means Brendan Rodgers’ side are now unbeaten in their last 10 league matches – a run that has seen them move to within just two points of fourth-placed Manchester United in the final Champions League spot.
Southampton will feel more than a little aggrieved not to have taken anything out of the game on a rain-drenched south coast and not for the first time this weekend, the man in the middle was the centre of attention after the full-time whistle.
Referee Kevin Friend was required to make a big call when Filip Djuricic, making his first start for Southampton, burst through on goal after just 30 seconds, only for Liverpool defender Emre Can to bundle the forward to the ground.
The official waved away the home side’s vehement protests and minutes later Liverpool were ahead, courtesy of a wonder goal from their impish Brazil international.
Picking up possession 25 yards out, Coutinho unleashed a fiercely struck effort that flew past a helpless Fraser Forster and into the back of the net off the underside of the crossbar.
Ronald Koeman’s men responded impressively to that setback, with Eljero Elia very nearly pulling them level straight from the restart following yet more appeals for a spot kick after a tug by Joe Allen on Djuricic, before a smart near-post stop with his feet by Simon Mignolet denied the Dutchman.
There was yet more controversy just past the half-hour mark when Sterling, who had returned to the Liverpool starting line-up after injury, appeared to be tripped in the box by Southampton captain Jose Fonte, only for Friend to again wave play on.
However, the officials did seem to get a crucial call wrong a minute before half-time when Elia broke clear of the visitors’ back four, only for the onrushing Mignolet to prevent the Netherlands international from equalising by handling the ball outside the area.
The linesman deemed the ‘keeper not at fault and Liverpool escaped, as they also did in first-half injury time when a third Southampton appeal for a penalty was rejected after the ball appeared to stike Dejan Lovren’s hand in the box.
After so many controversial incidents in the first half, it was almost inevitable the second period would be more sedate, and that is how it turned out as Southampton huffed and puffed, without ever threatening to get back on level terms.
And it was Liverpool who scored the killer second goal on 73 minutes after taking full advantage of a catalogue of errors by the home team, before Sterling fired home from six yards out for what was his third strike in as many games against the Saints.
Southampton tried to threaten a rousing finish, but the visitors’ impressive back line held firm to record a fifth straight clean sheet away from home in the league for the first time in 30 years.
Southampton: Forster (6); Clyne (8), Yoshida (7), Fonte (7), Targett (7); Wanyama (8), Ward-Prowse (5); Davis (5), Djuricic (7), Elia (7); Pelle (6)
Subs: Schneiderlin (7), Mane (8), Tadic (7)
Liverpool: Mignolet (8); Can (8), Skrtel (9), Lovren (6); Ibe (8), Henderson (7), Allen (7), Markovic (5); Lallana (6), Coutinho (6), Sterling (6)
Subs: Johnson (6), Sturridge (7), Moreno (7)
Man of the match: Martin Skrtel
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