José Mourinho ended up being sent to the stands in stoppage time, though this was still the kind of victory to make him purr. Manchester United are enjoying their best start to a campaign in six years even if a contest they had initially threatened to dominate, bullying their hosts into submission, went on to become a far sterner test of their resilience. Southampton rallied impressively after the interval and it was the visitors who were left clinging on, though their manager will still have delighted in rugged success.

Mourinho has always valued wins that have to be chiselled out and orchestrated shrewdly from the bench. He had flung on Chris Smalling and resorted to a back five before the end in an attempt to contain the hosts, Mauricio Pellegrino having exhausted his own team’s firepower from the bench. Even Fraser Forster ventured upfield at a set-piece while Mourinho was still shaking the hands of Southampton’s coaching staff having been sent to the stands, apparently for encroaching on to the pitch.

The final whistle would have sounded by the time he returned to the dressing room, leaving him to praise his team as “solid, with good solidarity, organisation and spirit, and amazing points”.

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It felt a significant win. Those around second-place United secured more riotous successes on Saturday but, in the manner it was achieved, this was arguably as impressive a result. Retreat to last season and United might have wilted, shipping an equaliser to record another of those horribly wasteful and familiar score draws. As it is they are four points better off than at the same stage last season having demonstrated they can scintillate or grind out results dependent upon the occasion. Phil Jones and Eric Bailly flung themselves at anything that moved, while Nemanja Matic and Marouane Fellaini offered a measure of authority in central midfield. Oriol Romeu should still probably have equalised, conjuring two headers and a shot wide of David de Gea’s far post having eased himself clear, but United heaved and succeeded in keeping their opponents blunted.

The management will wonder why their initial dominance had been eroded. “What pleased me was the pragmatism, but we were really tired at the end,” said Mourinho. “And nine of them didn’t play in midweek [in the League Cup], so for nine of them it’s not even an accumulation of fatigue. The weather was beautiful and even if you train at 11am, 12pm or 3pm in Manchester we don’t get this weather. Seriously. The last time we had this was in Los Angeles in preseason and then in Macedonia [for the Uefa Super Cup], and I think they felt [it]. I saw some players not sharp. Great spirit and always trying, but not the same sharpness.”

Facebook Twitter Pinterest José Mourinho is sent to the stands by the referee Craig Pawson. Photograph: Dylan Martinez/Reuters

That more than justified his late move to five at the back, once Manolo Gabbiadini had been introduced, and six in stoppage time.

Mourinho, sent to the stands against Burnley and West Ham last season, could offer no explanation for his own dismissal. He had been exasperated that too many of his players had ventured upfield on the counter, and appeared to enter the playing area before accidentally bumping into the fourth official, Mike Jones. “Craig [Pawson, the referee] told me to leave, so I left,” he said.

He was barely more forthcoming on the travelling support’s insistence on airing that infamous Romelu Lukaku chant once again, following it up with “We’re Man United, we’ll sing what we want”. The only terrace song Mourinho claimed to have heard was one from the Southampton fans telling him where to go, and described the travelling support as “amazing”.

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United’s rearguard ended up seeing them home, but Lukaku was their match-winner. The forward had bruised Maya Yoshida and Wesley Hoedt during a one-sided opening period and eventually scored his sixth goal in six Premier League games for his new club midway through the half.

Ashley Young patiently waited to squeeze space from Dusan Tadic on the flank before flinging over a cross to the edge of the six-yard box. Lukaku had already held off Hoedt, the Dutchman crumpling to the turf but not complaining of a foul, and Ryan Bertrand was in no position to choke his header. Forster did well to push that effort out, but the Belgian merely converted the rebound into the empty net.

Southampton had appeared fragile at that stage, but will take heart in how they recovered their poise – presumably to the satisfaction of the new owner, Gao Jisheng, who was watching for the first time from the directors’ box – for all that they have now gone scoreless in nine of their past 11 home league matches. They are “getting better”, according to Pellegrino.

As are United. “We are better this season than last, but this is nothing,” said Mourinho. “It’s just a start.”