Southampton won for the first time in 10 Premier League matches as Che Adams' spectacular strike helped Ralph Hasenhuttl's side claim all three points at Sheffield United, whose slim survival hopes took another blow at Bramall Lane.
Adams rifled a half-volley into the top corner four minutes into the second half, ending a run of 16 games without a goal in all competitions.
Saints, who lost Danny Ings to an early injury, had broken the deadlock when James Ward-Prowse sent Aaron Ramsdale the wrong way from the penalty spot following Ethan Ampadu's clumsy challenge on Nathan Tella.