After losing 1-0 to rival Bournemouth on Thursday, whose own relegation worries were further allayed, Southampton's 11-year run in the Premier League came closer to an end.
In the 50th minute, Marcus Tavernier squeaked a shot into the goal to hand last-place Southampton their 21st defeat in 33 league games this year.
Southampton is six points from safety with five games left, and it still has matches against both Newcastle and Liverpool, who are vying for Champions League positions.
The Saints have been in the top division since 2012, although they have spent the previous several seasons fighting relegation.
When many had Bournemouth pegged as a lock for an instant return to the lower-tier Championship, they have already won five of their past eight games to get out of danger.
The squad moved up to position 14, seven points above the bottom three.
Tavernier cut in from the right and fired a low shot that drifted slowly into the far corner for the game's only goal.