For more than half an hour, José Mourinho sat waiting on the Manchester United team coach outside St Mary’s doubtless basking in the comfort of a job well done after extending his side’s unbeaten run to eight matches. They displayed a callous efficiency and a charming stubbornness in an unforgiving and occasionally ugly performance that earned United victory and a fifth clean sheet in six Premier League matches. Romelu Lukaku, though, was still stationed inside in doping control, and, such is the ruthlessness of this United team at present, they left for Southampton airport without him.

Lukaku was ultimately the match‑winner but this was a result built upon steely foundations. Chris Smalling and Daley Blind offered late reinforcements and by the end United had six defenders on the pitch and sometimes eight, nine or even 10 men behind the ball. Lukaku was left estranged for large parts of the second half as a rejuvenated Southampton penned in the visitors.

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After hoofing the ball out of play and away from danger for a throw-in, Eric Bailly was triumphantly applauded by his manager. Marcus Rashford showed willing in both boxes while Phil Jones took an age to dust himself down after desperately – almost drunkenly – trying to shield the ball from Nathan Redmond, the Southampton winger.

For Mourinho, this felt like the sweetest of victories and reminiscent of those that helped him to the title with Chelsea in 2005. Ashley Young, the Manchester United full-back, insisted this “was not a United performance” – but his manager was delighted and not ashamed by it. As for the shift from stereotype, it would do United no harm whatsoever to have this sort of art up their sleeve.

As Mourinho was keen to emphasise afterwards, the prize for United was the same as after the 4-0 wins against Everton and West Ham United, regardless of the style in which they were achieved. United were plagued by 15 league draws last term, while they eked out only two 1-0 wins in the league last year (one of which was away, at Hull City in August) and Mourinho, more than anybody, knows the true weight of an ugly win or two. “Not always can you play really well,” Mauricio Pellegrino, the Southampton manager, said. “The best teams in the world adapt their players to every single situation.”

Indeed, Rashford and Juan Mata both had to do some dirty work. United are four points better off than this time last year but more pertinently appear to have rediscovered the swagger and the look of champions, an aura that has eluded them since Sir Alex Ferguson’s departure in 2013. Finding a way to win at Southampton on Saturday is further evidence of their marked progress, having been forced to settle for a draw at St Mary’s five months ago. United rode their luck a little this time around, typified by Marouane Fellaini’s clearance from Oriol Romeu’s goal-bound header, but there seems to be a belief that they will not shrink into their shells or go under, as they might have last season.

Such an underwhelming performance has inspired such overwhelming noise about United’s prospects this term. Mourinho, though, was reluctant to indulge in superlatives or to amplify talk of a title tilt but rather acknowledged the testing October period, during which they face Liverpool, Benfica and Tottenham Hotspur.

Beneath the surface, however, Mourinho must be feeling smug. At the heart of any title hopes are his go-to men, his trusty yet unfashionable players, such as Jones, Fellaini, Young and the captain Antonio Valencia, a couple of whom were ridiculed not so long ago.

Then there is the industry of Nemanja Matic and the once again impressive Henrikh Mkhitaryan, who was busy even if not at his best. Plus, it must be said, they missed Paul Pogba’s drive in midfield. And while Southampton deserve credit for putting the opposition on the back foot for most of the second half, on another day United could have ran away with it. Ander Herrera scooped harmlessly over while Lukaku should have doubled his tally, but for Fraser Forster.

Lukaku has certainly played his part, too. He has scored eight goals in as many matches and in doing so has reached that tally quicker than Eric Cantona, Ruud van Nistelrooy or Zlatan Ibrahimovic. The Belgian has slotted in so seamlessly that even Mourinho has expressed his surprise at the striker’s impact. “I knew he would score goals, more for us than he did for Everton or West Brom, that is logical,” Mourinho said, “but I was not expecting him match after match to put the ball in the net.” A trip to CSKA Moscow on Wednesday beckons and while it would usually be seen as a potential upset, this bruising, businesslike United are simply in no mood for slip-ups.