Philippe Coutinho and Raheem Sterling landed the killer blows that saw Saints slide out of the top four on Sunday afternoon, after contentious refereeing from match official Kevin Friend.
Friend put himself at the heart of the action after denying the penalty claims of Filip Djuricic in both the 1st and the 4th minute of the game, with Saints boss Koeman stating that he believed his side deserved at least one penalty.
Meanwhile, Friend denied Liverpool a penalty at the other end after a scything challenge from Saints captain José Fonte on Sterling, before turning a blind-eye when Simon Mignolet handled outside his area.
Coutinho opened the scoring in the third minute of the game, when he slammed in an impressive effort from 25-yards, putting Saints on the back-foot immediately as their visitors looked to soak up the pressure inside a vitriolic St. Mary's.
The match saw the return of Dejan Lovren, Adam Lallana and Rickie Lambert, and although none of the aforementioned players impressed, it nevertheless contributed to a feisty atmosphere on the south coast.
Eljero Elia and Djuricic, making his debut, had Saints' best chances in the first half, but were both thwarted by Liverpool goalkeeper Mignolet.
Ronald Koeman introduced fit-again Morgan Schneiderlin for Steven Davis at half-time, after a dismal first-half showing from the Northern Irishman, while Brendan Rodgers brought Alberto Moreno on in place of Lazar Markovic.
Some impressive inter-play between Saints shirts saw the ball break to Graziano Pellè, but instead of rolling the ball to Djuricic, who had found some space and was in on goal, the Italian scuffed a low attempt wide of goal.
Sadio Mané entered the fray in place of James Ward-Prowse after 59 minutes, and proved an immediate thorn in the side of the Liverpool defence, forcing Martin Skrtel into a vital block.
Former Saints captain Lallana was withdrawn after 62 minutes to raucous boos, after turning in a largely ineffectual display. Daniel Sturridge took his place, going up front in a move that saw Sterling move to a wide role.
After Dejan Lovren's first-half booking, Victor Wanyama became the second player in the book when he brought down Moreno in the 64th minute.
All hopes of a Southampton comeback were shattered when a defensive mix-up presented Sterling with a chance to double the away side's advantage, a chance that the England international would not pass up.
With 17 minutes remaining, Liverpool looked home and hosed against a Saints side that had rarely threatened Mignolet's goal in the second half.
Both managers made their final changes shortly after the goal. Rodgers opted to replace Jordan Ibe with Glen Johnson, while Ronald Koeman took off Djuricic to give a run-out to the Serbian midfielder's international team-mate, Dušan Tadić.
Moreno then went into the book for a foul on Elia, before Tadić's fierce low free-kick was held by Mignolet.
Jordan Henderson had a chance to put the icing on the cake for Liverpool when he received a ball from Moreno, but he was unable to convert.
Fraser Forster was called upon late on to deny Sturridge, in pursuit of that same honour, before a bicycle kick from Schneiderlin in the dying stages was gathered with ease by Mignolet.
Defeat saw Saints drop to 5th place, two points behind third-placed Arsenal.