Pressure on the Blades boss will continue to intensify in the days ahead as goals from Che Adams, Stuart Armstrong and Nathan Redmond sealed three points for the Saints.
Both teams struggled to settle into an early rhythm on a rainy south coast as Jan Bedranek powered a header wide and Sander Berge’s scuffed effort failed to test Alex McCarthy.
But with a scrappy theme beginning to develop before the break the Saints did edge in front through Adams.
James Ward-Prowse’s free kick was headed back into the box and Adams was more determined than John Egan as he bundled past Aaron Ramsdale.
Not being able to keep Southampton out before the break dented United confidence after the restart as Ralph Hasenhuttl’s team went through gears.
Armstrong extended their lead on the hour as his deflected strike trickled past Ramsdale.
That left the Blades chasing shadows in the closing stages as Redmond tucked home a deserved third with five minutes left.
He linked up cleverly with Oriol Romeu on the edge of the box and with no Blades defender tracking his run he confidently slotted past Ramsdale.
Full Time at the St. Mary’s Stadium it’s Southampton 3 Sheffield United 0