Ronald Koeman’s side looked to be heading for a fourth consecutive game without a win until Mane’s chip broke the deadlock late on.
The Senegalese’s effort was his sixth goal of the season and Southampton’s first goal in four home games lifting them into fifth place in the Premier League.
Mane was quickest to respond when substitute James Ward-Prowse saw his effort spilled by Julian Speroni after some neat footwork.
Palace headed into the game on the south coast off the back off the back of a 3-1 win away to West Ham.
The Eagles came closest to breaking the deadlock through a mistake from Southampton goalkeeper Fraser Forster.
The England international fumbled a cross in 36th minute which almost fell to Wilfried Zaha, but the former Celtic keeper managed pounce on the loose ball.
In what was a quiet first half the best chance fell to goal shy Graziano Pelle, but the Italian who failed to score in the league this year squandered the opportunity.
An Eljero Elia strike from a corner stung the fingers of long serving Palace goalkeeper Julian Speroni.
Pelle was quickest to respond but the forward couldn’t divert his effort goal bound and break his barren run.
The game sprung into life in the second half as two chances in quick session from Crystal Palace tested Forster.
First Palace broke from a Southampton corner, with the ball falling to Yannick Bolasie. The winger’s effort was palmed away by Forster into the path of Jason Puncheon.
Puncheon played a cute through ball into the path of Zaha. The former Manchester United player struck the ball across the goal beating Forster but hitting the post.
Southampton responded with a chance of their own. Maya Yoshida flicked wide substitute corner Dusan Tadic just after the hour mark, in what was the closest Southampton had come in the second half.
Southampton continued to probe but failed to find the back of the net. Their best chances came through set pieces as a Tadic effort in the 76th minute just flew over the bar.
Southampton looked to be heading for a fourth home game without a goal, breaking a club record but Mane’ persistence kept their Champions League hopes alive.
Saints move up to fifth, two points off third and a point off fourth.