Three left-footed strikes took Saints from two goals down to a 3-2 victory on a dramatic afternoon at St. Mary's.
Ronald Koeman made just one change from the team that won 2-1 at Stoke City last weekend, with José Fonte coming in for Matt Targett.
Victor Wanyama only made the bench after returning from a five-game suspension.
Shane Long had an early appeal for a penalty rejected, when after racing through on goal Long appeared to be fouled by Dejan Lovren, who put his arm across the back of Long and clipped his legs as the pair ran for the ball.
The visitors then took the lead when Philippe Coutinho curled an effort past Fraser Forster from outside the area in the 17th minute.
Just five minutes later Liverpool had doubled their lead, with Divock Origi leading a break-out before teeing up Daniel Sturridge to finish inside the far post from the right-hand side of the penalty area.
Forster turned away a shot from Joe Allen, who witnessed a strike hit the back of the net just moments later, only for it to be chalked off after Mamadou Sakho was offside and adjudged to be interfering in play.
The half-time interval saw Koeman make two changes, with Victor Wanyama and Sadio Mané replacing Jordy Clasie and Dušan Tadić.
The pair proved to have a massive impact on the turnaround, as Saints began to dominate the encounter and create more goalscoring opportunities.
Saints were presented with a golden chance to pull one back when referee Roger East pointed to the spot after Graziano Pellè was felled by Martin Skrtel, but Mané's low penalty was saved by Simon Mignolet.
The Senegalese forward bounced back in fine fashion, though, pulling away from his marker before firing a left-footed effort across goal and beyond Mignolet in the 64th minute.
James Ward-Prowse was deployed as Koeman's final substitution, with Oriol Romeu making way after a solid display.
The crowd at St. Mary's were lifted and roared once more when Pellè's curling strike beat Mignolet from outside the area with just seven minutes remaining.
Further euphoria was soon to follow, with Mané wheeling away from Sakho before striking the ball into the far side of the net to complete the comeback with just four minutes left on the clock.
Victory takes Saints three points above Jürgen Klopp's men in the table, with seven games of the season still to play.
Next up for Saints is a trip to league leaders Leicester City after the international break.
Saints: Forster; Martina, Fonte, Van Dijk, Bertrand; S. Davis, Clasie (Wanyama - 45'), Romeu (Ward-Prowse - 69'), Tadić (Mané - 45'); Long, Pellè.
Unused Subs: Stekelenburg, Cédric, Yoshida, Juanmi.