The Lilywhites demolished newly-promoted Burnley 5-2 just before the international break, while the Blades picked up their first point in a 2-2 draw at home to Everton.
Match preview
The infamous Giorgio Chiellini clip began doing the rounds on social media once again when Spurs' EFL Cup journey ended with a penalty-shootout loss to Fulham in the second round, which closed off one avenue to a long-awaited trophy, and Postecoglou's side fell behind with just four minutes on the block against Burnley to Lyle Foster's strike.
However, Son Heung-min's delicate chip and a Cristian Romero thunderbolt turned the game on its head before the break, and the former completed a heroic hat-trick in the second half after the effervescent James Maddison had picked out the bottom corner with aplomb.
Josh Brownhill doubled Burnley's tally for the afternoon with seconds remaining, but there was no raining on the Tottenham parade as Spurs made it 10 points from a possible 12 in the 2023-24 Premier League season, cementing a second-placed standing in the table as a result.
Having scored at least two goals in all of their Premier League games under Postecoglou so far - 11 in total to be exact - Tottenham have only been bested on the points tally by Manchester City, while Brighton & Hove Albion are the sole team to net more times than the Lilywhites with 12 efforts to their name.
With hitherto struggling midfielders being given a new lease of life and old faces in attack shining, Spurs could hardly be in a better position heading into their first North London derby at the Emirates on September 24, while a mouthwatering home clash with Liverpool is also on the menu at the end of the month.
Everton number one Jordan Pickford was both Sheffield United's best friend and worst enemy at Bramall Lane two weeks ago, as Abdoulaye Doucoure scored the Toffees' first Premier League goal of the season before Cameron Archer's crisp finish restored parity for the Blades, who then went ahead thanks to an enormous stroke of luck.
A second Archer strike hit the post before cannoning into the net off Pickford's back - akin to Emiliano Martinez's own goal versus Arsenal back in February - but Arnaut Danjuma crashed home at the back post to level the scores for Everton, who were then indebted to Pickford for an unbelievable double save to deny Oli McBurnie right at the death.
While Paul Heckingbottom's side were left to rue what could have been, one point was still an improvement on their first three Premier League fixtures, and the 17th-placed Blades are keeping their heads above water for the time being thanks to the goal difference column.
Sheffield United and Spurs can also empathise when it comes to early EFL Cup eliminations, as the Blades succumbed to Lincoln City's 12-yard superiority before clinging on for a point against Everton, and four of the visitors' last five competitive away matches have now ended in defeat.
Spurs also strolled to a pair of 3-1 and 4-0 wins over Sheffield United during the 2020-21 Premier League season before the Blades' demotion, but the Lilywhites were condemned to another year without silverware by Heckingbottom's side only six months ago, as an Iliman Ndiaye strike knocked Tottenham out of the FA Cup in the fifth round.
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Sheffield United Premier League form:
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Team News
As will be the case with numerous Premier League teams, Tottenham will need to carefully assess their international contingent, in particular Son, Romero and Richarlison, the latter of whom recently revealed that he plans to seek psychological help following a challenging time off the field.
Son and Romero both shook off injury scares during the international break, and the pair's importance to Postecoglou's formation cannot be overstated, but they will arrive back at Hotspur Way following taxing journeys home from Asia and South America respectively.
Rodrigo Bentancur (knee), Bryan Gil (groin), Ryan Sessegnon (hamstring) and Alfie Whiteman (ankle) are all recovering from operations, while Giovani Lo Celso missed Argentina's fixtures this month with a thigh strain and is touch-and-go for the weekend too.
While Sheffield United's international contingent did not travel so far and wide, the Blades have no fewer than eight injury concerns to contend with for the weekend after losing Yasser Larouci to a back injury midway through the second half against Everton.
The 22-year-old - who has recently pledged allegiance to Algeria - has not been ruled out of the trip to North London just yet, but Leicester City loanee Luke Thomas could now come into the XI, especially with Ben Osborn also sidelined with a severe groin injury.
Daniel Jebbison (illness), Max Lowe (ankle) Rhys Norrington-Davies (thigh) and John Fleck (calf) are all expected to sit this one out too, while there are question marks over Anel Ahmedhodzic (hamstring) and Rhian Brewster (thigh), but John Egan shook off a knee concern to represent the Republic of Ireland during the international break.
Tottenham Hotspur possible starting lineup:
Vicario; Porro, Romero, Van de Ven, Udogie; Sarr, Bissouma; Kulusevski, Maddison, Solomon; Son
Sheffield United possible starting lineup:
Foderingham; Basham, Egan, Robinson; Baldock, Hamer, Souza, Norwood, Thomas; Archer, McBurnie
We say: Tottenham Hotspur 3-0 Sheffield United
The international break undoubtedly came at a better time for Sheffield United than a Tottenham team with the wind in their sails, but we can only see Postecoglou's lively crop picking up where they left off.