The Blades are through to the second round of the FA Youth Cup after a thrilling penalty shoot-out against Oldham Athletic at Boundary Park on Wednesday night.
Otis Khan, who later saw red in extra-time for a second bookable offence, netted twice for United, whilst Jordan Bove scored both of the Latics goals in Lancashire.
U18s coach Travis Binnion commented: "We showed an excellent spirit against committed opposition in horrendous weather conditions. We know we can play much better in possession, however the lads showed real character and found a way of winning, which we believe was just about deserved over the whole game after Oldham were the better team in the first half.
"Otis Khan showed real quality again with his two goals and goalkeeper Jake Eastwood was excellent throughout."
On a wet night in Lancashire, coaches Chris Morgan and Andy Garner were in attendance to see the Blades youngsters in action and they were quick to impress, opening the scoring in the first ten minutes when Cockerline flicked on for KHAN to race on and beat the home goalkeeper with a right-foot shot.
Good defending from Evans and a number of saves from goalkeeper Eastwood, kept Oldham out before the break, whilst there were chances to extend the lead but Heh and Reed were denied.
Calvert-Lewin went close early in the second half but two moments of misfortunate allowed Oldham to level on 55 minutes. Firstly, they were handed a throw-in which they were not entitled to and then in the same move Banton slipped, conceding a penalty, which BOVE converted.
Dimaio and Wright attempted to restore United's lead, with the visitors clearly on top as the 90-minute mark approached and late on a header from Evans was cleared off the line.
The first period of extra-time was eventful after Eastwood made a tremendous save to deny Walters, who also saw an effort come back off a post. However, Oldham did take the lead on 96 minutes when BOVE added his second.
Oldham's advantage lasted just a matter of minutes, though, as KHAN also added his second with a 20-yard curling free-kick after Coustrain's run was unfairly halted.
Khan had an opportunity to add a third in the second period of extra-time but when he was dismissed for a second bookable offence, the numerically disadvantaged Blades settled for the lottery of penalties.
And it proved to be a good decision as goalkeeper Eastwood saved twice and Whiteman, Wright, Coustrain and Dimaio all scored to secure a 4-3 shoot-out win.
A home tie now awaits United, with one of non-league trio Worcester City, Rugby Town or Halesowen Town set to provide the opposition.
Blades: Eastwood, Paling, Ptak, Reed, Evans, Banton, Calvert-Lewin (Coustrain 59), Dimaio, Cockerline (Whiteman 105), Khan, Heh (Wright 59). Unused: Scarisbrick, Owen.