David McGoldrick made the difference precisely converting a penalty after Jack O’Connell was manhandled in the penalty box in the second half.
Tigers showed improvement from their tame surrender at home to Leeds on Tuesday, but the loss to Sheffield means they have won once in nine games and are now bottom of the pile.
With Chris Wilder having named an unchanged starting XI for a fourth consecutive game, it was not surprising that Sheffield United, who just got promoted to the Championship this season, were soon on the front foot.
The home side came close after just six minutes when Chris Basham's cross from the right bamboozled Reece Burke, whose uncertainty nearly gifted Enda Stevens a tap-in.
The visitors' cause was also hindered by an injury to striker Fraizer Campbell, who was replaced by Nouha Dicko on the half-hour mark.
Hull made a fleet-footed start to the second half, with Dicko's strike off an astute Chris Martin flick-on nicely saved by Dean Henderson at his near post.
Henderson later produced a much more significant stop when he parried Markus Henriksen's header away for a corner.
Sheffield United also had their moments – Billy Sharp hooked Kieron Freeman's header wide after 61 minutes – but they lacked the necessary gold-dust where it mattered.
That was until McGoldrick sent Marshall the wrong way with a sweetly-taken spot-kick.
Hull defender Tommy Elphick felt he should have been given a late penalty for a similar offence that saw his team punished, but referee Peter Bankes dismissed the claims as Wilder's well-organised team edged to victory.
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