Morgan Schneiderlin put the hosts ahead in the second half, after being the better side during the opening 45 minutes, but an ex-Saint broke their hearts after a defensive error
After a first half in which the home side dominated, but failed to break through, they finally found the net when Morgan Schneiderlin got on the end of a Rickie Lambert flick on, and was left with a simple finish. However, a former Saint, Nathan Dyer, came back to haunt the south coast outfit, stealing the ball from Maya Yoshida before netting the equaliser.
Jack Cork started for Saints for the first time this season, after recovering from an ankle injury, with 17-year-old Luke Shaw making his full Premier League debut at full back and Jason Puncheon returning.
Meanwhile, Michael Laudrup was still without Kyle Bartley, Neil Taylor, Michel Vorm and Chico Flores so named an unchanged line-up with ex-Saint Gary Monk captaining the visitors.
Though Swansea dominated possession in the opening stages, it was Saints who created all the early chances. Schneiderlin blasted over from the edge of the box after good work from both Rickie Lambert and Puncheon. Then, Adam Lallana was denied by a brilliant Gerhard Tremmel save, Lambert involved once more, and Gaston Ramirez curled just wide.
Ki Sung-Yong stung Paulo Gazzaniga's palms with a powerful strike just after but it was the hosts who went on to threaten more regularly in the first half, Ramirez going close again after the Swans surrendered possession on the edge of their own box.
The Uruguayan was in much better form than his last outing, and continued to pose a threat as he won a free kick off Ashley Williams. He took it himself and deceptively chipped it to Jose Fonte at the back post, the defender's strike being blocked.
Saints' pressure continued after a quiet spell just after the re-start, with Ki sliding in to deny Lambert from shooting inside the penalty box and Monk then throwing himself in front of a Ramirez effort.
However, the dominance finally told just after the hour mark when Yoshida pumped a long ball into the Swans' area which Lambert flicked on, wrong-footing Hemmell and leaving Schneiderlin with a straightforward finish into the empty net.
But, with Saints' defence notorious for leaking goals this season, a clean sheet was too much to ask for. Ten minutes late Gazzaniga put his own defender, Yoshida, under real pressure with a poor clearance. The Japanese then failed to get rid of the ball before former Southampton winger Dyer, on as a substitute, stole the ball and finished past the keeper.
Lambert flashed a header just wide moments after, with Lallana having a penalty appeal turned away as well as the home side searched for a winner.
However, it could have also turned out worse for Saints had it not been for a last-ditch sliding block from Yoshida, keeping the well-earned point safe and lifting them off the bottom of the table.