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Following a low-key start, Eljero Elia had the first shot of the night on five minutes, but his effort soared high above the bar.
Midway through the first half, a penalty appeal for Palace was waved away as Dwight Gayle tumbled under a challenge in the box.
Just after the half-hour mark, the Eagles nearly broke the deadlock when Fraser Forster dropped a Yannick Bolasie cross with Wilfried Zaha set to capitalise, but the Saints stopper did enough to get back and keep the ball out.
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Southampton ended the first 45 minutes on a high as Elia burst in late on and fired in a low shot towards goal, but Julian Speroni got down well to make the save.
The visitors went on to register their first shot on target after the restart when Bolasie's cross from the left was met by Jason Puncheon, whose shot was defiantly punched away by Forster.
Moments later, Jose Fonte failed to clear his lines properly, hesitating for too long and allowing Zaha to control and fire a shot that bounced off the far post.
Maya Yoshida was next to threaten as he stuck his foot out in the box to try his luck at bundling a corner in at the far post, but he managed only to steer the ball wide.
However, Southampton's endeavours paid off late on when, in the 83rd minute, substitute James Ward-Prowse's effort from the left was spilled by Speroni, and Mane was at hand to lift the ball over the keeper and into the net.
The result puts the Saints back into the top five of the Premier League table, while Palace sit 12th.