The victory over last season's League Cup winners was their third win in a row and saw them register a fifth clean sheet in seven league matches, form that has kept them in fourth spot and only behind third-placed Chelsea on goal difference.
Southampton weathered plenty of attacking pressure from their opponents at St Mary's, but on the back of goalkeeper Artur Boruc's strong display their line remained intact, with goals in each half by Adam Lallana and Jay Rodriguez, their first in the league since April, enough to give them their fourth win from seven outings.
Rickie Lambert's call-up to the England team at 31 and the £12.8 million pounds signing of Dani Osvaldo from AS Roma have dominated the south coast club's headlines, but Lallana said it was a solid defensive foundation that was the basis for their success.
"We know we haven't scored (since Reading) but it's nothing we've been too worried about because we've been picking up good results and keeping these clean sheets, which is keeping the pressure off players like myself and the strikers, who then only need one goal and take 1-0s," Lallana told the club's official website (www.saintsfc.co.uk) after the match.
"Fortunately, today Artur was in great form, some of the saves he made were brilliant, he was really consistent and as I said, for the team it makes things so much easier because if you keep clean sheets then you're going to get at least a point out of the game."
Michu, Wilfried Bony and Nathan Dyer all had chances for Swansea, who beat St Gallen in the Europa League on Thursday, but the scoreline could have been even greater had Kenyan Victor Wanyama not had a goal chalked off for a foul.
It continues a remarkable resurgence for the club, who reached the Premier League last season after a seven-season absence, having been in the third tier) as recently as 2010-11.
Despite leading them to two consecutive promotions Nigel Adkins was dumped as manager in January with Mauricio Pochettino replacing him - a move that seemed risky at the time but has since paid handsome dividends.
Pochettino secured their Premier League status and has taken them to greater heights this term, as well as having them playing a pleasing brand of soccer.
"We didn't play as well as we wanted to, but we got the result we wanted," the Argentine said after the match.
"We were able to withstand their attacks, so we've learned how to execute a certain phase of football today."
"We have to keep trying to establish how we want to play football, and I think we did that today.
"I am very happy for everyone involved with the club and all of the fans, but we've only just started - we need to keep working as hard as we are right now."
($1 = 0.6221 British pounds)