The old maxim about concentrating for the full 90 minutes is long dead, and with Peter Bankes adding a minimum of 12 minutes to the second half and the visitors under siege as they clung to Gustavo Hamer's goal, it was always going to be a real test of weary legs and minds.
Oli McBurnie receiving a second yellow card for throwing his man to the ground in the 14th minute of overtime just rubbed salt into gaping wounds.
For the second time in three games, Paul Heckingbottom's side had looked on the verge of a smash-and-grab, only to have it snatched away from them.
For all their dominance, until Richarlison lost Chris Basham at a corner to glance in, followed up by Kulusevski's shot through Jack Robinson's legs, Spurs had been frustrated by defending bordering on fantaticism.
At that stage, they also seemed to be fighting Lady Luck but she came to their aid at the death.
When Sheffield United first came to this stadium, in November 2019, they left cursing the video assistant referee. Four years on it looked like they would head home thanking Graham Scott.
The Blades had defended with great discipline for half an hour, Basham – in the side because John Egan was missing his first league game through injury that month – doing a good job of following James Maddison when he dropped into midfield.
But when Maddison was in the area in the 31st minute, the captain for the day took the ankle of his standing foot in a good position for Bankes and his linesman to see. Nothing was given.
If Graham Scott looked at it again from Stockley Park – there was no indication he had but surely he must have – he did not see anything wrong.
After David McGoldrick's harshly VAR-disallowed goal for a John Lundstram offside an eternity before in the build-up, the Blades might have thought they were owed that.
They had certainly done a good job until then in the way they did at home to Manchester City. It might be unambitious, but the Blades are operating in the real world.
They kept Spurs at arm's length early on. The only efforts inside the first 17 minutes were both weak from Pape Matar Sarr. A backpedalling Christian Romero headed off target at a corner.
Only when Yves Bissouma burst past Vincius Souza and Basham in the 21st minute was Foderingham made to earn his wages. A curling Son Heung-min shot forced another good save.
When Manor Solomon made him stretch after breaking through a tackle, the pressure was increasing and Basham's tackle could have been the release but forutnately the VAR was not playing ball.
On a couple of occasions the Blades suggested they might just be able to throw a counter-punch, McBurnie's shot hitting Cameron Artcher and his header right at the end of the first half straight at Gugleilmo Vicario.
In a rare contribution on his return to the club, James McAtee forced a decent save in between, but Jayden Bogle had been over-eager in his run, and was flagged offside.
The pressure on both the Blades and referee Bankes ramped up throughout the first 25 minutes of the first half.
Robinson's 69th-minute booking was the most baffling of all, apparently trying to kick a quick free-kick against Son. Play was stop when the South Korean retrieved it, and Robinson presumably booked for kicking the ball away. Maybe.
It added to the sense that the home fans had been expressing earlier to Bankes – "You don't know what you're doing."
Minutes earlier Souza had pushed Bissouma in the back. Perhaps the midfielder's theatrical fall saved the Brazilian, but it looked like another escape.
Sarr, Maddison, Pedro Porro and Micky van de Ven all tried their luck.
McBurnie threw himself in the way of a Son shot almost immediately after being booked, Robinson blocking the follow-up. Anel Ahmedhodzic put his head int he way of a Kulusevski effort and Robinson smothered another strike from the winger. Foderingham had earlier taken a clattering , not that the home fans were very sympathetic – unhappy with the tardiness of his restarts.
It told in 12 minutes added to the second half.
Battered, the Blades were unbowed, and when nobody else managed to get a touch on Robinson's long throw in the 73rd minute, Hamer calmly side-footed in his second goal for the club. He must like this dayglo yellow kit.
Spurs retaliated with a triple substitution and one of them, Brennan Johnson, had the ball in the net but like Bogle, he had mistimed his run by a fraction.
In days gone by, Foderingham's 90th-minute save from Kuluseviski might have been a match-winner but this game had plenty of time to run.
Even with so much of the extra period gone when Richarlison headed in, you always felt Spurs, with a raucous stadium behind them, could snatch a winner and so it proved, the Blades losing the ball on their left and Kulusevski making the space to find the net.
Tottenham Hotspur: Vicario; Porro (Emerson 90+4), Romero, van de Ven (Hojbjerg 90+4), Udogie; Sarr (Perisic 79), Bissouma; Kulusevski, Maddison, Solomon (Richarlison 79); Son (Johnson 79).
Unused substitutes: Skipp, Dier, Forster, Davies.
Sheffield United: Foderingham; Bogle (Trusty 86), Basham, Ahmedhodzic, Robinson, Thomas; Souza, McAtee (Norwood 69), Hamer (T Davies 79); McBurnie, Archer.
Unused substitutes: A Davies, Traore, Slimane, Larouci, Seriki.
Referee: P Bankes (Merseyside).