Goals have been hard to come by for Saints at St Mary’s in recent weeks and their goal drought looked set to extend as Graziano Pelle wasted a glorious chance just before the break.
Ronald Koeman’s side rode their luck after the break as Crystal Palace hit the post through Wilfried Zaha but the hosts finally made the breakthrough in the 83rd minute as Mane pounced on Julian Speroni’s error to give his side all three points.
The strike inflicted Crystal Palace’s first defeat on the road under Alan Pardew and moved Southampton back up into fifth, just one point behind Manchester United in the race for fourth.
Saints were seeing plenty of the ball but looked like a side lacking in confidence as first Eljero Elia fired wide, before Filip Djuricic blasted over the bar from just inside the box after Victor Wanyama’s blocked shot fell into his path.
Crystal Palace were coping well with the Southampton threat but failed to offer much themselves.
However, Fraser Forster nearly gifted the visitors the opening goal of the game, dropping Bolasie’s hopeful cross but the England keeper just recovered in time with Zaha waiting pounce.
The chance of the half fell to Pelle as Speroni saved Elia’s deflected shot. The ball fell to the feet of the Italian just five yards out, but he looked like a man who has not scored in 10 Premier League matches, prodding his shot wide.
Since taking over at Selhurst Park, Pardew had not tasted defeat away from home and he sent out his side with renewed purpose after the break as Zaha’s cross found Jason Puncheon in the box, but the forward’s shot was straight at Forster.
The visitors continued to press forward and went closest to breaking the deadlock as Bolasie’s shot was blocked by Forster but the rebound fell to Zaha, who struck the far post with his shot.
Koeman responded by sending on Dusan Tadic and the move had the desired effect as Southampton grabbed a foothold in the game once again, creating half chances for Djuricic and Pelle.
It looked like it was going to be more St Mary’s woe for Southampton when Maya Yoshida failed to get a good connection on Pelle’s flick on with the goal at his mercy.
But the gloom around the stadium was lifted when substitute James Ward-Prowse beat his man on the edge of the penalty area to fire a left-footed shot on goal which Speroni could only parry.
The ball rebounded into the path of Mane, who made no mistake in firing home to score Southampton’s first home goal in five hours and 87 minutes of football and get Koemen’s side back to winning ways.
Palace threw on Shola Ameobi in a desperate bid to rescue a point and he fluffed his lines heading Joe Ledley’s cross wide. The visitors had one final chance to level but Yoshida was on hand to make a vital block when Bolasie looked poised to pick out a team-mate in the dying stages.
But Southampton held on for their 13th Premier League clean sheet and a much needed win to move ahead of Liverpool into fifth, while Palace stay in 12th, eight points above the relegation zone.
See all the goals from Tuesday’s games on Sky Sports News HQ from midnight.
Phil Thompson’s verdict
Southampton are still struggling to score goals and hit the target. Ward-Prowse showed fantastic ability with a run through the middle,
Speroni spilled it and Mane chipped it in, but I think this should have been a draw because Palace did enough to get a point.
Southampton: Forster (7), Clyne (6), Yoshida (7), Fonte (7), Bertrand (6), Schneiderlin (6), Wanyama (6), Mane (7), Elia (6), Djuricic (7), Pelle (6).
Southampton subs: Long (5), Tadic (6), Ward-Prowse (7).
Crystal Palace: Speroni (5), Kelly (6), Delaney (6), Dann (6), Ward (6), McArthur (6), Ledley (6), Zaha (6), Puncheon (7), Bolasie (7), Gayle (6).
Crystal Palace subs: Ameobi (5).
Man of the Match: Saido Mane