For as hard as Rushden & Diamonds toiled to secure their third-round replay they were seriously aided and abetted by the troubled First Division side.
The Blades chairman, Derek Dooley, notches up his 70th birthday today, but will he have the heart to raise a glass in celebration? Scarcely, as he contemplates the poisoned chalice that has become the Bramall Lane chairmanship.
Worse, of course, may follow when these less than dashing Blades visit Nene Park a week tomorrow for the second instalment. Yet, paradoxically, this was the result the Diamonds manager, Brian Talbot, did not want for a club whose main aim is to graduate to the Football League.
By hook or by crook, United seemed determined to make sure they were going to get it, and by way of complicity missed a 66th-minute penalty. That curious piece of action made a hero out of the former Northampton goalkeeper, Billy Turley, who dived to his right to save from Jonathan Hunt.
However, the kick was executed with so little conviction that Mrs Turley might have been hard-pushed not to have fallen on the ball.
With that penalty miss came redemption for defender Paul Underwood, whose handling offence presented Hunt with a golden opportunity.
Such is life at Sheffield United, a club sinking in a sea of debt and with a penchant for self destruction. With a little more due care and attention, though, they could have driven safely into the fourth round.
They started brightly and appeared to have too much for the Diamonds, whose defence seemed seriously flawed. But instead of running away with the tie they put away just one of the huge pile of chances they created in a one-sided opening half, when Marcus Bent rose unchallenged to head in Paul Devlin's deep cross.
The new manager, Neil Warnock, must have thought that was game, set, if not exactly match. "But instead of burying them we gave Rushden so many lifts," complained Warnock, who cut his own managerial teeth in the non-League scene with Scarborough.
The biggest of those leg-ups was arranged a minute before half-time when the Australian midfield player, Jon Brady, crossed from the left, but instead of gathering safely goalkeeper Simon Tracey inexplicably allowed the ball to slither through his grasp, conceding an unlikely equaliser.
Talbot, whose up-and-coming team gave Leeds United of the Premiership a fright at the same stage of this competition last season, confirmed he could do without the replay. However he insisted: "I believe we have the character and resilience to cope with the extra demands. In the end our goalkeeper was the hero but I think we had several heroes out there."
Goals: Bent (14) 1-0; Brady (45) 1-1.
Sheffield United (3-5-2): Tracey; Derry, Murphy, Ford; Devlin, Ribeiro (Hamilton, h-t), Hunt (Smeets, 79), Woodhouse, Quinn; Smith (Kachuro, 79), Bent. Substitutes not used: Cullen, Duke (gk).
Rushden & Diamonds (4-4-2): Turley; Wooding, Rodwell, Warburton, Underwood; Brady, McElhatton, Butterworth, Burgess (De Souza, 67), Town (Heggs, 89), Collins. Substitutes not used: Hamsher, Mison, Smith (gk).
Referee: B Knight (Orpington).
Bookings: Sheffield United: Woodhouse, Hamilton. Rushden: McElhatton.
Man of the match: Turley.