With Mauricio Pochettino’s visitors widely considered to be safe from Premier League relegation, they will have been pleased to extend their unbeaten run to six matches and sit eight points clear of the drop zone.
Michael Laudrup’s Swansea, meanwhile, will be disappointed to fail to win a fifth successive game in a slump at the end of the season but they remain in the top half.
Swansea had made a promising start, with their movement causing the visitors problems without creating any clear-cut opportunities.
But Pochettino’s men grew into the game, with the industrious Jack Cork forcing Michel Vorm into the game’s first save with a hopeful effort from the edge of the box.
Vorm continued to be the busier goalkeeper and had to be at full stretch to deny Rickie Lambert his 15th goal of the season, the Dutchman tipping over a free-kick that was arrowing into the top corner.
But the goalkeeper blotted his copybook seconds later, failing to hold a simple Jay Rodriguez cross for Adam Lallana to bundle in, only for the whistle to go for handball against the Saints midfielder.
Laudrup removed Luke Moore at the break and introduced Wayne Routledge in a bid to find some inspiration.
The change almost paid dividends just two minutes after the resumption but Michu could not keep his header down from the winger’s cross.
Swansea went closer still shortly after when Lallana let the ball run loose inside his own area and Michu pounced to set up Nathan Dyer, but Maya Yoshida got himself in the right place to clear off the line.
Southampton dropped ever deeper and packed midfield as the pressure increased and Daniel Fox survived an ambitious handball appeal as he blocked substitute Ki Sung-yueng’s volley.
Artur Boruc then made two excellent saves as he denied Jonathan de Guzman and Dyer when the pair were in on goal.
And with time running out the visitors almost snatched a winner. Ki was muscled off the ball by Steven Davis, but Vorm sharply held Emmanuel Mayuka’s effort.