Meanwhile, Slavisa Jokanovic's Blades overcame Carlisle United before dumping Derby County out of the tournament to book their place in this stage.
The less said about Sheffield United's start to life back in the second tier the better, although the Blades are slowly but surely starting to demonstrate their promotion credentials and marched to a convincing 3-1 win over Hull City on Saturday afternoon.
Ageless talisman Billy Sharp drew first blood with a 17th-minute header before defender John Egan netted a rare brace in the second half to put the Blades out of sight, while Keane Lewis-Potter's 74th-minute strike for the hosts proved to be nothing more than a consolation.
Now unbeaten in five across all competitions, Sheffield United have found their golden touch at just the right time - scoring 13 goals during their hot streak - although Jokanovic claimed that his side could have shown more of a "killer spirit" at the weekend.
A 1-0 triumph over Carlisle preceded a 2-1 success over fellow Championship side Derby in the EFL Cup for the Blades, who renew hostilities with the Rams - now in administration - four days after the visit of Southampton, while Middlesbrough also lie in wait before the end of the month.
Should Sheffield United progress to the fourth round of the EFL Cup this week, it will mark their best-ever run in the tournament since their memorable run to the semi-finals in 2014-15, but Southampton have already proved their prowess in this competition.
On another day, Ralph Hasenhuttl's plucky side could have travelled home from the Etihad with all three points in the bag, as a Saints penalty - and red card for Kyle Walker for a foul on Adam Armstrong - was controversially overturned by VAR in front of City's joyous supporters.
However, the champions' home crowd had little to cheer about for the remainder of the afternoon as Southampton claimed a highly credible draw against the champions, who had previously trounced Everton, Norwich City and Arsenal by three successive 5-0 scorelines at the Etihad before being nullified by Hasenhuttl's men.
While holding Pep Guardiola's men to a goalless draw is no mean feat, Southampton remain winless in the new Premier League season - drawing four of their opening five games and losing the other to Everton - but the St Mary's faithful will not be forgetting their 8-0 EFL Cup second-round thrashing of Newport County in a hurry.
Southampton famously reached the final of the 2016-17 EFL Cup before being sunk by a Zlatan Ibrahimovic-inspired Manchester United, and they have failed to make it past the fourth round since then - suffering defeats to Leicester City and Man City at that stage in 2018-19 and 2019-20 respectively.
During their two most recent seasons in the Premier League, Sheffield United suffered four consecutive defeats against Southampton by an aggregate scoreline of 9-1, and Hasenhuttl's side eased to a 2-0 win at Bramall Lane as recently as March.
Sander Berge suffered a hamstring tweak before the win over Hull and is unlikely to be passed fit here, while Enda Stevens, David McGoldrick, Lys Mousset and Jack O'Connell also occupy spots in the treatment room.
Liverpool loanee Ben Davies also had to be taken off in the dying embers of Saturday's game, but his substitution was only thought to have been precautionary.
Southampton, meanwhile, remain without Stuart Armstrong and Theo Walcott for the time being due to calf and muscle problems respectively, but Will Smallbone has made a long-awaited return to team training from a knee injury.
Mohamed Elyounoussi's hat-trick against Newport in the second round reignited his Saints career, but the Norwegian or Nathan Redmond may drop out here as Nathan Tella and Moussa Djenepo hope to be given opportunities to impress.
Chelsea loanee Armando Broja will also hope to benefit from some rotation to start up top, while new arrival Lyanco could be handed his debut for the club in the heart of defence after Jack Stephens went off injured against City.
Sheffield United possible starting lineup:
Foderingham; Bogle, Basham, Egan, Robinson; Norwood, Guedioura; Burke, Ndiaye, Brewster; McBurnie
Southampton possible starting lineup:
Forster; Valery, Lyanco, Salisu, Perraud; Elyounoussi, Diallo, Ward-Prowse, Djenepo; Broja, Adams
We say: Sheffield United 0-1 Southampton
In spite of their winless start to the new Premier League season, Southampton have certainly posted some respectable results, although they are highly unlikely to have as much luck in front of goal as they did against Newport here.
Sheffield United are not to be taken lightly as they begin to gather momentum under Jokanovic, but as heavy rotation on both ends takes effect, we expect Southampton's winning streak against the Blades to continue with a narrow success en route to round four.
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