Two extra-time goals from Jordan Slew helped United book a place in the quarter-finals of the FA Youth Cup.
Against Premiership Blackpool in front of 828 fans in the fifth round tie at Bramall Lane on Wednesday night, John Pemberton's young Blades were impressive.
After Liam Tomsett had given Blackpool the lead, substitute Connor Martin levelled to send the game to extra-time before Slew netted a double to secure a deserved-victory.
In a frantic start, there were three chances in the opening six minutes. Tomsett's free-kick was pushed away by Long as the visitors went close, whilst all of United's early chances fell to Whitehouse, he shot over the top and then headed against the outside of a post from McFadzean's corner.
Skipper Whitehouse also went close on 21 minutes but he headed wide Gregory's cross, whilst Slew was the recipient of heavy challenge from goalkeeper Kettings.
The chances dried up through the mid-point of the half but the Blades were clearly on top and forcing the visitors back, particular down the right-flank.
On 38 minutes a cross from Montgomery saw Ironside get in front of goalkeeper Kettings but couldn't direct his header, whilst on the stroke of half-time Kennedy was unmarked from Gregory's corner but headed wide.
United began the second period well and continued to force the visitors back. The Blades thought they had taken the lead on 49 minutes, only to be denied by an offside flag. From Anderson's cross, Ironside's header was clawed out by Kettings and after a melee, Gregory slotted home before his celebrations were cut short by the officials.
Whitehouse went close again on 54 minutes, shooting at goalkeeper Kettings, before the home side were struck by a cruel blow just three minutes later. Ironside squandered possession and Barkhuizen laid off for TOMSETT to calmly sidefoot beyond Long's right-hand to give the visitors an unlikely lead.
Slew was squeezed out as he looked for a leveller and Whitehouse's cross was cleared as Harriott was poised to head towards goal. There was another dangerous moment when Blackpool's Dodd fired a free-kick wide before United finally beat Kettings after 74 minutes.
Substitute MARTIN had only been on the field five minutes when he raced through a gap in the Blackpool defence and his shot evaded the left-hand of the goalkeeper at the Kop end.
Anderson's free-kick was saved by Kettings as United went in search of a winner and Martin and Whitehouse had a late chances but the game headed to an extra period.
However, with the first attack in extra-time, the Blades finally grabbed the advantage on 94 minutes. From a free-kick by Anderson, Maguire's header was well kept out by Kettings, but SLEW was on hand to force home the rebound.
The impetus remained with the Blades in extra time, although Kennedy was called on to make a timely tackle before the teams switched ends once more.
Three minutes of the second period of extra-time had elapsed when Slew doubled his tally and put the game beyond the visitors. Martin supplied the cross from the right and after holding off Challinor, SLEW fired passed the exposed Kettings.
Blackpool, expectedly, attacked more in the remaining minutes but Long's goal was not over duly troubled and the Blades celebrated at the final whistle.
Blades: Long, Montgomery, Anderson, Harriott, Maguire, Kennedy, Gregory (Wilkinson 65), Whitehouse (Hinchliffe 103), Ironside (Martin 69), Slew, McFadzean.
Unused: Barry, Willis.
Blackpool: Kettings, Challinor, Roberts, Tomsett, Mitter, Younda, Barkhuizen, Jobe (Cross 90), Gratton (Tchobanian 58), Dodd, Francis-Reynolds.
Unused: O'Connor, Hunt.