United's U21s will play Huddersfield or Millwall in the Professional Development League 2 play-off final after beating Charlton Athletic at The Valley on Monday afternoon.
The Blades trailed at half-time after Terell Thomas headed the Addicks in front, but a second-half penalty from Diego De Girolamo, after David Brooks was fouled, sent the game into extra-time.
And De Girolamo poked home the decisive goal seven minutes into the additional half hour to see the Blades advance, with the home side finishing the game with ten men after Thomas saw red in the final moments.
United started positively, McGahey headed over before Kimarni Smith had a headed saved from a corner inside the opening 20 minutes. But the Blades then fell behind as THOMAS looped in a header of his own from a inviting free-kick from Charles-Cook.
The final 15 minutes of the first-half was very much nip and tuck and although Charles-Cook looked a big threat for the Addicks, the visitors regrouped after conceding and defended resolutely for the remainder of the first period.
Despite being behind and having less possession, it was United who looked the biggest threat in the second period and they levelled just after the hour.
Brooks broke clear of the home defence but as he barred down on goal his progress was halted by a combination of goalkeeper Mitov and Umerah and the referee instantly pointed to the spot. DE GIROLAMO stepped up and fired into the bottom corner.
The Addicks finished strongly in the final 20 minutes, but despite the best efforts Hanlan and Umerah, the scores remained level at full-time, meaning extra-time would be needed to find a winner.
And seven minutes into the additional 30, the Blades edged themselves in front as DE GIROLAMO capitalised on a defence error by Thomas before slotting past the advancing Mitov.
Understandably, the home side threw everything at United in search of a goal that would have taken the clash to penalties and Eastwood was at his best late on to deny Ahearne-Grant, saving superbly from a free-kick.
In the third minute of stoppage-time at the end of the second period of extra-time, the game finished in an unsavoury manner, as Thomas saw red for a stamp on Eastwood, which led to unnecessary scuffle between both sets of players.
But it wasn't going to stop United celebrating as the final whistle was sounded, as John Dungworth's side followed in the steps of Travis Binnion's U18s in securing a final berth in the end of season play-offs.
Blades: Eastwood, Cummings, Kelly, Kennedy, McGahey, Semple, Reed, Gilmour, De Girolamo, Brooks (Brown 109), K. Smith (Hall 82).
Unused: Charlesworth, Ramsdale, Hallam.