Philippe Coutinho and Daniel Sturridge had given the visitors a commanding lead going into half-time, but Graziano Pelle and a Sadio Mane brace ensured the points would remain on the South Coast despite Mane's missed penalty.
Saints revert to four at the back
The home side opted for a back four for the second consecutive match after changing from a preferred from a back five that has regularly been seen this season. Ronald Koeman only made a single change from the win at Stoke City, bringing Jose Fonte back into the side with youngster Matty Targett making way.
Saints started slowly and the visitors took advantage of that with Coutinho running the show. He fired a shot just outside the post, followed by delivering a cross for Emre Can to head at goal but Fraser Forster saved comfortably.
Coutinho and Sturridge strike
Jürgen Klopp’s men continued to put pressure on the Saints, and it prevailed as Coutinho picked up the ball some distance outside the box and fired a low driven shot across goal into the far corner to give the visitors the lead.
The Merseyside outfit then doubled their lead as Daniel Sturridge netted his third goal against the Saints this season.
The ball was in the Saints net again shortly but the flag was up and was rightly ruled offside to prevent further damage.
Koeman wasn’t happy at half time and rolled out the changes, bringing Victor Wanyama and the influential Sadio Mane on, replacing Jordy Clasie and Dusan Tadic.
Mignolet preserves Liverpool's lead
Five minutes into the second half the changes seemed to kick in as Southampton were awarded a penalty after Martin Skrtel pulled down Pelle and referee Roger East pointed to the spot. Mane stepped up but was denied by a fantastic save from Simon Mignolet.
The penalty miss seemed to get under Mane’s skin and surged him and Saints forward. It reaped reward when Pelle sent him through and he calmly finished to pull a goal back and give the home fans hope of a revival.
Saints then threw the kitchen sink at Liverpool trying to find an equaliser, forcing Mignolet into numerous saves to keep them at bay. With seven minutes to play, Pelle unleased a powerful curling shot with his left foot, across the goalkeeper and into the far corner past the despairing Mignolet.
Mane seals the comeback
Momentum was pouring out of the home side now, and they went charging for a winner. They found what they were looking for when a string of errors by the Reds defence allowed Mane time and space to compose himself and put home the winner and trigger an eruption of noise around the ground.
This victory leaves Saints just three points behind the Europa League qualification places and the manner in which they won this game could hand Koeman’s men momentum to put a string of wins together to catapult them up the table.
Southampton travel to league leaders Leicester City after the international break and hope to spoil the party for their own aspirations.
It all could have been different for Saints, due to the game changer Mane, who was sent off last week at Stoke but fortunately his ban was overturned in time for him to play against Liverpool.
His pace and skilful dribbling put the Liverpool defence on edge every time he got the ball. With the Italian Pelle re-finding his feet back in the side, this could be the start of a fruitful partnership.