Alfie Mawson's first-half header gave Paul Clement's team the lead and, after Shane Long drew the Saints level, the hosts' talisman Gylfi Sigurdsson secured a vital three points for the struggling Swans.
It is a result which allows Swansea to move away from the relegation zone, while Claude Puel's side face a long trip home after another lethargic and disappointing away performance.
Hosts can't get helping hand early
With the Swans languishing perilously close to the relegation zone and Southampton having one of the worst scoring records in the league, it came as a surprise to no one when the opening exchanges provided little goalmouth action. Shane Long wasted a half-chance from a tight angle and Gylfi Sigurdsson's low drive was blocked when the ball broke kindly for him, but that was the closest either side came to breaking the deadlock in the opening 15 minutes.
It was just after the quarter of an hour mark when the first real talking points of the game arrived. After referee Roger East waved away optimistic Swansea penalty claims for a potential handball on Cedric Soares, the resulting corner led to far stronger appeals.
Fernando Llorente met Sigurdsson's delivery, getting the finest of touches to divert the ball onto the arm of Southampton centre-back Jack Stephens. However, East adjudged this handball to be accidental also, denying the hosts a penalty for the second time in a minute. Although it was far from a blatant penalty, the Saints defence would have undoubtedly been thanking their lucky stars after this decision.
Swansea take the lead
Despite the controversy, the game was not sparked into life until the back end of the first half. A Leroy Fer volley forced a decent low save out of Southampton goalkeeper Fraser Forster and, from the corner that followed, Swansea centre-back Alfie Mawson met Sigurdsson's teasing delivery. Saints midfielder Oriol Romeu did manage to get his head in the way of the 23-year-old's goal-bound header, but he could only divert the ball into his own net, giving Clement's men a much-needed lead.
Just before half-time, a neat turn by Sigurdsson gave him enough space to unleash a left-footed effort from the edge of the area, but Forster was equal to his deflected effort. Nevertheless, the Swans went into the break with a deserved 1-0 lead against a Saints side who had been a devoid of creativity going forward.
Saints draw level
It took exactly 57 minutes for Southampton to construct a decent attacking move but when they did, they were rewarded for it handsomely. A delightful threaded ball from Steven Davis played left-back Ryan Bertrand in behind the Swansea defence, and he curled an inch-perfect low cross to give Long the simplest of finishes. Out of nothing, Puel's men were level.
The equaliser allowed the visitors to begin to assert their dominance over their relegation-threatened opponents. Just moments after Long's goal, a Southampton counter resulted in substitute Sofiane Boufal laying off Nathan Redmond inside the box, but he skewed his shot way off target, with the ball embarrassingly going out for a throw in. The Englishman came a lot closer soon after, forcing a fantastic save from Lukasz Fabianski to keep out his powerful long-range strike.
The perfect counter-attack
Just as it looked like the Saints were going to make their spell of pressure tell, they found themselves behind again. A corner for the away side was cleared to Swansea debutante Luciano Narsingh, who used his searing pace to work space for a cross from the left, which found the unmarked Sigurdsson. The Iceland international duly made Southampton pay, getting just enough on his volley back across Forster to restore his side's advantage with little over twenty minutes to go.
Predictably, the Swans were the subject of a barrage of late pressure from Southampton, but were able to hold off the visitors' desperate attempts to find a second equaliser in the dying minutes. Besides the lively Boufal, the Saints were uninspiring, and they were left with that all too familiar feeling of frustration at not producing enough going forward.
For Swansea however, a second win in a row gives them a little bit of breathing space between them and the bottom three, meaning things are all of a sudden looking up in South Wales.