Charlie Austin's 64th minute winner was no more than the Saints deserved, after an amalgamation of bad luck, last-ditch defending and poor finishing had kept an underperforming Southampton side in the contest.
The result ensures the morale on the South Coast is lifted, and the pressure on new manager Claude Puel very much relieved with this success stringing back-to-back wins together in all competitions.
Saints switch it up again
Southampton made several changes in the week as they opened their Europa League campaign with a home victory against Sparta Prague, and Puel's selection to face Swansea was no different. The Frenchman varied his side again, making six changes to the victorious starting XI last Thursday, including returns for captain Jose Fonte and striker Nathan Redmond as they searched for their first league win of the season.
Swansea meanwhile, just made a single change from the team that drew with Chelsea a week ago. Moudou Barrow came in for the perhaps unpopular Neil Taylor, after an ostentatious touchline dispute with manager Francesco Guidolin when he was substituted before half time in the Chelsea game. Swans' midfielder Jack Cork, who spent four years at Southampton, captained the Welsh side for the second week in a row.
Having done the double over Swansea last season, it was perhaps unsurprising to see Southampton dominate possession in the opening exchanges. However, the hosts couldn't create more than a handful of chances in the first 20 minutes, coming closest with a shot from Shane Long on the edge of the penalty area being parried away by Lukasz Fabianski, before a combination of Steven Davis and Dusan Tadic were flagged offside as they tried to scramble in the rebound.
Moments later, Fabianski was called upon again; comfortably tipping over a dipping Tadic free-kick.
The away side slowly began to grow into the game, and carved out their best opportunity of the first period on 25 minutes, as Barrow's cross from the right-hand side found Fernando Llorente, but the Spaniard couldn't make any meaningful contact from close range.
Having been on the receiving end of a controversial penalty decision last weekend against Arsenal, the Saints were left feeling frustrated again five minutes before half-time. as Swans centre-back Federico Fernandez appeared to bring down Long inside the box as the ball was heading out of play. However, referee Mike Jones saw the incident as simulation by the Irishman, booking Long and giving a free-kick Swansea, rather than a spot-kick to Southampton.
Motivated by what was in their eyes an injustice, Puel's side launched an unsuccessful enslaught on Fabianski's goal in the dying minutes before the break. Redmond, without a goal since the opening day of the season, wasted two glorious opportunities.
The 22-year-old first drilled a shot from close range just wide after being played in from the right. A couple of minutes later, he received an even better opening having been put through by Tadic, but despite some decent footwork and only having Fabianski to beat, Redmond could only blaze over the bar. This was almost the last act of a 45 minutes dominated by Southampton, leaving them wondering how they could not break the deadlock before half-time.
Even after just five minutes for the second-half, it already seemed like it was just not going to be Southampton's day. The Saints' dominance continued, as if the interval had never taken place, and opportunities came instantly. First a deft touch from Long beat Fabianski, but was desperately cleared away by the covering Kyle Naughton.
With their next attack, the Long had the ball in the net, but Redmond was ruled offside in the build-up. Southampton's fortune up to this point was summed up when replays showed the Englishman to be level with the last Swansea defender.
When substitute Charlie Austin rattled the bar from point-blank range on the hour mark, once could have been mistaken for think there was a force field around the Swansea net.
Breakthrough at last
And then, like a dam finally giving way under a tremendous amount of pressure, the goal the home side's play deserved eventually came. With the crossbar still rattling from his previous effort, Austin got on the end of a deflected Tadic cross, chested the ball down, before firing emphatically past Fabianski on the volley to give Southampton the lead. This continued the good form of the man singed from Queens Park Rangers last January, as he increased his tally for the season to three following a brace against Sparta Prague just a few days ago.
With the relief of 30,000 Southampton fans reverberating around the ground, they watched their side remain on the front foot following Austin's strike. However, they could not double their lead during their latest spell of pressure, meaning a nervy final few minutes would have to be endured before the hosts could celebrate their first Premier League three points of the campaign.
With five minutes to go, the heart-rate in St Mary's increased substantially. Swansea had hardly threatened all game, but when the ball fell kindly for Gylfi Sigurdsson inside the opposition penalty area, it took a brilliant save from Fraser Forster to prevent the midfielder's low shot from giving the visitors what would have been an undeserved point.
Besides this major scare, Southampton saw the final stages of the game out relatively comfortable, sealing their first clean sheet since February and, more importantly, that elusive first league win under Claude Puel.