The winger poked home from close range to end the Eagles' fine run of away results and in turn reignite the Saints' hopes of a Champions League berth alive
Filip Djuricic wasted the best chance of the first half as he blazed over the crossbar from the edge of the box.
But the visitors were far more adventurous in the second period, and almost broke the deadlock themselves as Wilfried Zaha struck an effort against the post.
With time running out, however, the Saints secured the three points as Mane converted from close range after Julian Speroni could only parry a shot from James Ward-Prowse.
Mane had been the last man to find the net for Southampton in a 1-0 triumph over QPR on February 7, and this late strike ended Palace's sequence of five successive away victories in all competitions since Alan Pardew took charge.
The former Southampton boss had enjoyed a 3-2 success at St Mary's Stadium in the FA Cup fourth round as part of that run, but his side could not build on their impressive 3-1 win at West Ham on Saturday.
Victory lifts Southampton above Liverpool into fifth place, while Palace drop a place to 13th, still eight points clear of the drop zone.
Palace were forced into three changes due to Jordon Mutch's thigh injury and the suspensions of Glenn Murray and Mile Jedinak after their transgressions at Upton Park.
Djuricic - recalled as one of two changes following his side's defeat at West Brom - had the first opportunity of the game when he fired over from just inside the area in the 11th minute.
The hosts survived a scare 10 minutes before the break when Fraser Forster dropped Yannick Bolasie's cross under little pressure, and just managed to re-gather the ball before Zaha could stab it into the net.
Southampton ought to have been in front five minutes later, but Graziano Pelle prodded wide from close range after Speroni parried Eljero Elia's initial shot.
Palace offered little going forward in the first half, but almost made the breakthrough three minutes after the interval when former Southampton man Jason Puncheon turned and fired a shot straight at the legs of Forster.
The visitors came even closer to scoring in the 55th minute as Bolasie and Zaha both threatened an opener.
Initially, Forster denied Bolasie and, as Southampton failed to clear, the DR Congo international fed Zaha, who struck a low shot against the inside of the post before the hosts finally scrambled the ball away.
Midway through the half, Maya Yoshida could only divert the ball wide from close range after meeting Pelle's flick-on from a corner.
With time running out, Speroni made a mess of Ward-Prowse's shot, and Mane reacted quickest to lift the ball over the prone goalkeeper and into the net.