United had the ball in the net in the opening 20 minutes, from Matt Done’s header, but it was ruled out for offside.
But there was no denying the Blades, who took the lead when Ethan Ebanks-Landell headed in John Fleck’s corner.
United thought they had made it 2-0 when Fleck’s long-range effort hit the back of the net.
But the officials deemed it had hit Billy Sharp - standing offside - on the way and the goal was chalked off.
United got the second goal their first-half display warranted when defender Ebanks-Landell volleyed home as the ball bounced around in the area.
Amazingly, United had a third goal ruled out for offside at the start of the second half, Duffy’s cross picking put Done who tapped home at the Kop end, but once more referee Mark Heywood halted play.
It was 3-0 on 62 minutes. United broke, as Vale pushed bodies forward, and had four against two.
The ball was played right to Sharp, whose initial shot was blocked, but it fell to Mark Duffy who had time to pick his spot with defenders on the line.
Sharp was denied again, by the offside flag, which seemed another marginal decision.
Sheff Utd: Moore, Wright, Ebanks-Landell, O’Connell, Freeman,
Coutts, Duffy, Fleck, Lafferty, Done, Sharp. Subs: Hussey,
Scougall, Lavery, Ramsdale, Brown, Whiteman, Chapman.
Port Vale: Alnwick, Purkiss, Streete, Smith, Knops, Jones,
Amoros, Grant, Hart, Foley, Paterson. Subs: MacIntosh, Cicilia,
Mbamba, Turner, Kiko, Pereira, Miguel Santos.
Referee: Mark Heywood (Cheshire)
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