Yeates scored a superb solo effort early in the second half to make it nine goals for the season for the Blades and light up a dull game between the league's two lowest scoring sides.
Clear-cut chances were at a premium throughout the clash, with substitute Jamie Ward coming close to a second for the Blades, who moved above their opponents with the win.
The Tigers made one change from the side which drew 1-1 at Leicester on Saturday, with Kevin Kilbane coming in for Rowan Vine.
Stephen Jordan returned to the Blades' line-up in place of the injured Ritchie De Laet.
Hull were straight onto the attack, with Mark Cullen seeing a shot blocked by defender Chris Morgan after just 40 seconds.
City went on to dominate the early stages, with Robert Koren, who was on the scoresheet at the weekend, volleying wide after good work from Richard Garcia.
It was all Hull as Daniel Ayala tried his luck with two shots from distance in quick succession, while Garcia forced the first save from Steve Simonsen with a 20-yard drive.
Ayala found himself in the referee's notebook in the 36th minute for a late challenge on Stephen Quinn as the game continued to lack flow.
There was a flurry of chances towards the end of the half, though, with Sheffield United striker Richard Cresswell forcing Matt Duke to push away a header after he connected perfectly with a Yeates corner.
Quinn saw a 25-yard effort comfortably gathered by Duke, while at the other end Cullen shot wide from 12 yards when well placed.
The first real moment of quality in the game brought the opening goal in the 53rd minute as Yeates embarked on an excellent jinking run which took him into the box and he coolly slotted home.
The goal prompted Hull boss Nigel Pearson to make a triple change, with Vine, Jay Simpson and John Bostock coming on for Cullen, Garcia and the ineffective Caleb Folan.
Bostock was straight into the action, but his audacious free-kick from 35 yards cleared the crossbar.
A long-range volley from Yeates failed to trouble Duke, while sub Ward almost sealed victory for the visitors with six minutes remaining when he lashed in a drive from the edge of the box which was parried to safety by the keeper.
The closest Hull came to a last-gasp equaliser was a weak header from Paul McShane which drifted wide and a shot from Bostock which was easily dealt with by Simonsen.