The hosts started the game brightly, with Sadio Mane curling an effort just wide early on, before Steven Davis blasted a speculative long-range effort wide two minutes later.
In the 11th minute, the Potters threatened through Peter Crouch when he got onto the end of Steven N'Zonzi's cross, but the England forward failed to find the target.
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.