The game started off very slow with both sides having no chances until 13 minutes in when on loan midfielder from Celtic Jon-Paul McGovern handed the Blades a goal. His left footed shot from 18 yards out deflected into top corner.
The Minstermen came close to a leveler, Jagielka brought Duffield down in front of goal but Brackstone's free-kick went straight to Kenny.
On half hour Potter hit a shot wide for the visitors and McGovern's corner came to nothing.
Both sides had little chances and the closest United came was on 38 minutes when Robert Kozluk's shot fired high over the bar.
Moments later United won a free-kick when Hobson brought down Peschsolido, McGovern took it but was saved by Northern International Alan Fettis.
Half-Time: Sheffield United 1-0 York City
At half-time no changes were made by Sheffield United or York City.
United started off really quick with Iffy Onoura's shot being saved just two minutes after re-start. A minute later Tonge had a chance and again was saved by Fettis.
Not long after that Peter Duffield's effort was saved by Paddy Kenny.
On 53rd minute Jon-Paul McGovern's corner was met by the head Jagielka but just went over cross bar.
After 58 minutes the first substitute was made when Carl Asaba came on for Canadian International Paul Peschisolido.
On 67 minute mark York's Calverho came on for Nogan.
Later on United had a few chances but came to nothing while York managed one effort but was denied by Kenny. Peter Duffield headed just wide after Porter crossed.
With just over 15 minutes to go Brackstone's corner was met by the head of Bullock but was cleared off the goal line by Murphy.
A few minutes later the Blades made their second change, with Michael Brown making a entrance in way of Nick Montgomery.
With 10 minutes to go another McGovern's corner found the head of Iffy Onoura but just went over.
A few minutes later Asaba nearly got the second but just shot wide. And with a minute left Yelcin came on for Potter.
In last minute young defender Ben Doane came on for Michael Tonge, but was too late as the full time whistle went.
Full-Time: Sheffield United 1-0 York City
Man of the Match: I think that the MOTM award will go to Jon-Paul McGovern due to his hard work in the game and also he scored the winner.