Ole Gunnar Solskjær knows a thing or three about impact substitutions but even Manchester United’s former supersub extraordinaire must have been pleasantly surprised to see Romelu Lukaku step off the bench and score with his first touch.

Until the Belgian’s game-changing intervention, Solskjær had seemed outwitted by Rafael Benítez’s contain-and-counter tactics yet by the end of a bitterly cold Tyneside night the impressive Marcus Rashford had added a second to make it four victories from four for José Mourinho’s interim successor.

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It makes the Norwegian the first Manchester United manager since Sir Matt Busby to win his opening quartet of games. Perhaps instructively, he acknowledged it would be “hard” for him to relinquish the role and return to his “day job” at Molde in Norway during May. “Of course I won’t want to leave,” he said, semi-teasingly. “I don’t want to.”

His smile suggested he knows he will almost certainly have to – although much more of this and all bets will be off.

In marked contrast, Newcastle United have won only two home games all season and are just two points above the relegation zone. If Manchester United’s flight to the warmth of Dubai on Saturday evening for a mid-season training break should be a happy one, Newcastle have no reason for similar relaxation.

Benítez was left rueing the rare goalkeeping error from Martin Dubravka which prefaced Lukaku’s opener. “We have to be disappointed in the way we lost,” he said. “We were very close to getting something but then we made a mistake and we paid for it.”

Solskjær’s principal success seems to have been liberating the creative imaginations of players cowed and cramped by Mourinho. Accordingly as the visiting full-backs, Antonio Valencia and Luke Shaw, pushed forward against Benítez’s five-man defence and Dubravka scrambled an awkward early Rashford shot to safety, it felt as if it might be a long night for Newcastle.

Play Video 0:58 'I don't want to leave': Solskjær jubilant after Man Utd win at Newcastle – video

Things certainly appeared to have changed since the last time Solskjær patrolled the away technical area here in the spring of 2014; back then Alan Pardew’s Newcastle won 3-0, confirming Cardiff’s relegation from the Premier League.

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Not that the Norwegian could afford to relax as he surveyed a backline which could easily have conceded an early goal when Phil Jones’s ill-advised back pass played Salomón Rondón onside and the hitherto noisy travelling fans congregated high in the Leazes End temporarily fell silent.

Ultimately, Jones recovered to rescue the situation but Benítez had a glimmer of optimism.

Granted, only Dubravka’s astute positioning prevented Rashford from scoring after Jamaal Lascelles and Fabian Schär collided in their own area and Paul Pogba regularly advanced down the inside-left channel with destructive intent, but the visiting side’s final ball was not quite coming off.

Neither was Newcastle’s but at least Christian Atsu used his pace to good effect down the home left, exploiting the space often left by Valencia’s swashbuckling attacking advances. The problem was that when presented with two half chances, Atsu directed the first shot straight at David de Gea and sent the less than perfectly controlled second flashing across the face of goal.

Facebook Twitter Pinterest Phil Jones’ inch-perfect tackle denies Salomón Rondón. Photograph: Serena Taylor/Newcastle United

Another half chance saw Rondón connect with a decent Atsu cross but Jones’s presence seemed to restrict his leap and the resultant header flew harmlessly over the bar.

The watching Alan Shearer might have scored in that situation but at least Rondón was giving Solskjær’s defenders reason to curb their attacking inclinations. That mattered, particularly as, at the other end, Lascelles’s style had also been cramped, albeit for a different reason, namely the yellow card he received for a wince-inducing challenge on Ander Herrera.

If Lascelles had enjoyed gently roughing up Rashford, Jonjo Shelvey, a second-half home substitute, contributed a couple of defence-bisecting, outside-of-the-boot passes but was lucky to stay on the pitch after a high late challenge with which he caught Pogba on the back of a knee with studs raised.

That incident should not detract from Benítez’s commendable gameplan. Tellingly the increasingly urgent little chats Solskjær and his assistant, Mike Phelan, had been holding with Juan Mata and company during breaks in early second half play emphasised that Newcastle had succeeded in denying their guests room for fluid attacking manoeuvre.

An unlikely hero in this collective masterclass in the art of assiduous closing down was Matt Ritchie. Newcastle’s right-wing-turned-left-wing-back proved intelligence and industry personified as he worked to restrict the threat from Valencia and Mata.

The moment had come for Solskjær to liberate Lukaku and Alexis Sánchez from the bench and when Dubravka uncharacteristically spilled Rashford’s dipping 25-yard free-kick Lukaku reacted with alacrity, scoring with his first touch by responding faster than Lascelles to drive the rebound over the line.

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Time remained for an unmarked Rashford to slide a shot through Dubravka’s legs at the end of a move he had started himself. It involved Lukaku cueing up Sánchez, who marked his return from hamstring trouble with a pass which not only picked out Rashford but also rekindled visiting hopes of a top-four finish.

“Marcus has a great hit,” added Solskjær after presiding over his first clean sheet. “He must have been watching Cristiano [Ronaldo] practising. Without hitting the heights it was a very professional performance.”