Many might have expected the Saints to be blown away on a windy day at St Mary’s, but they competed well with Mateus Fernandes getting an early shot off while Conor Bradley and Ibrahima Konaté were lured into bookable challenges.
The Reds started to get regular shots off after the 20th minute, although Alex McCarthy denied Mohamed Salah, Dominik Szoboszlai, Cody Gakpo and Curtis Jones.
The goalkeeper was soon beaten, though, as his choice to roll the ball to Fernandes started a passage of play that culminated in Flynn Downes gifting possession to Szoboszlai, whose brilliant shot went in off the post.
Southampton suffered another blow with Adam Lallana going off injured but still got their lifeline when Andy Robertson fouled Tyler Dibling on the edge of the box to concede a penalty.
Caoimhín Kelleher’s save from Adam Armstrong’s initial spot kick was eventually deemed futile as the striker followed up to convert.
Southampton were let off after conceding possession in the box again moments after the equaliser, although they suffered more injury disappointment as Paul Onuachu was forced off following an impressive first-half display.
Undeterred, Dibling did brilliantly to find Armstrong, who laid the ball off for Fernandes to score with a clinical first-time finish.
That momentum was halted nine minutes later, though as McCarthy rushed out to meet Ryan Gravenberch through ball but was beaten to it as Salah diverted it over the line.
The goalkeeper then tipped Luis Díaz’s header over but was then let off by Gravenberch after failing to punch the ball away, before Alexis Mac Allister’s strike fizzed marginally wide.
Yukinari Sugawara then handled in his own box within five minutes of coming off the bench, conceding a penalty that Salah emphatically converted.
While the Egyptian couldn’t complete his hat-trick with a late strike crashing against the post, his spot kick earned Liverpool’s fifth consecutive win across all competitions and take the Reds eight points ahead atop the PL table.
That also condemned Southampton to back-to-back defeats despite their valiant efforts.