Chances were few and far between for the visiting side from the Steel City but went away with all three points for only the second time this season after Danny Webber's solo goal at Leicester City won the game.
And following a corner Webber chipped back in for an unmarked Gary Cahill to head home on the stroke of half-time whilst with ten minutes remaining it was a backs to the wall job as the Blades kept City at bay to hold on to the lead.
The victory put United up into 12th position with just two points behind and in front of Barnsley and Sheffield Wednesday maybe now Bryan Robson; who has been under fire from the Blades faithful may now be taken seriously.
It does seem amazement as to why United have had a turn in fortune which could be a number of deciding factors; a) moving three upfront which he has moved back to two following difficult opposition, b) injury to Paddy Kenny at Leicester has lead to Ian Bennett taking between the sticks, or c) Robson wearing a tracksuit instead of a suit which has made him more passionate and lead the team from the front.
Whatever the reason it has worked with the Blades spurting up the table after a six game unbeaten run which started on 20 October with a 1-1 draw with Preston NE, since then they have claimed points against; Leicester City (1-0) Hull City (1-1), Burnley (0-0) and Ipswich Town (3-1) which has seen them take in twelve points.
Stoke City set off the game with electrifying pace and overall maybe would have done enough for a point on another day; and they could have gone ahead before United but the Blades showed great strength and resilience to keep their towering strike force of Mamady Sidibe and Ricardo Fuller at bay.
Fuller was the home teams main danger and made stand in keeper Ian Bennett earn his crust as the former Birmingham City shot stopper was forced to make a few brilliant saves which kept United in the game and on course for the victory.
On 20th minute mark Fuller came very close to breaking the deadlock but he fired over the top after John Eustace had put him through.
As the game grew the visiting team become stronger and wit minded in attack, and following masterful play by Webber the Blades almost took the lead through David Carney.
Danny Webber worked well the right hand side before turning his marker on the edge of the area, he delicately chipped across for the Australian to chase down and smash against the near post and out for a goal kick.
But, a minute later the Blades won a corner; Carney floated over from the right hand side which City keeper Steve Simonsen failed to catch, Webber turned and crossed back in for Gary Cahill to head unchallenged into the net!
In the second half City once again came out all guns blazing but to no prevail as a strong United back four was a s solid as a rock with Cahill pulling out all the stops to prevent a Potters backlash.
The front two men at the Britannia Stadium were causing havoc with Fuller and Sidibe without really testing Bennett. Jonathan Parkin was brought onto the field by manager Tony Pulis and the former Barnsley and Hull forward soon made his mark; producing a spiralling pass to free Fuller but Cahill came in at the least to prevent a sure goal.
Jamaican international Demar Phillips was also brought on with eleven minutes remaining in a desperate attempt to draw the game level, they all pilled forward and failed to break the deadlock as United soaked in unbearable pressure as City won string after string of corners which United somehow kept out.