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The hosts started the game brightly, Mane curling an effort just wide early on, before Steven Davis blasted a speculative long-range effort wide two minutes later.
The goalmouth action continued just after the quarter-hour mark when Victor Moses marauded through the Saints backline, but the Nigerian striker's subsequent shot was weak and easy for Fraser Forster to collect.
Just moments later, it was Southampton's turn to come forward with Mane driving to the byline before picking out Graziano Pelle at the front post, but the Italian striker's shot flew over the bar.
The imminent breakthrough eventually came the way of the hosts in the 33rd minute when Pelle latched on to the ball inside the box and struck the post with a decent effort, with Mane firing the rebound home from close range.
Southampton picked up from where they left off in the second half, Tadic swinging a ball from the right flank towards Pelle, who subsequently smashed a headed effort against the crossbar.
Jonathan Walters threatened for Stoke just before the hour when he fired wide from the edge of the box, but this proved a rare effort for the visitors as the Saints resumed their assault on the Potters goal, Pelle and Tadic firing shots on goal in the 66th minute.
In the 78th minute, Phil Bardsley did well to bring the ball forward, lofting in a near-perfect cross for Mame Biram Diouf, but the ball proved an inch or two ahead of the Senegalese who was sliding in.
Nevertheless, the hosts were able to see out the game and secure three valuable points to climb to second in the table, with Stoke in 11th place.