A ruthless streak has been restored to Manchester United’s approach after all. José Mourinho had seen his team’s dominance yield only draws too often of late, but here they did what this club used to do as a matter of course.

Just as the prospect loomed large of shedding points to a Crystal Palace team most among the elite will consider there for the taking, class told. Their progress feels more serene when an unbeaten league run is extended to seven games by successive victories, however narrow.

This win was chiselled from the visitors’ most dominant period of play, the winner created by the contest’s most influential performer and scored by a forward who has always delighted in stamping his influence all over occasions such as this.

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Paul Pogba capitalised on Yohan Cabaye’s slip two minutes from time to gain possession and consider his pass, sliding his delivery beyond Scott Dann and along the edge of the penalty area. There darted Zlatan Ibrahimovic, timing his diagonal run perfectly, with his finish dispatched crisply beyond the on-rushing Wayne Hennessey from an unkind angle and into the net.

It was an eighth goal in as many games for the Swede, whose influence on this side should not purely be measured in terms of that impressive tally. “I told him this isn’t the best place to play if you’re looking for holidays,” said Mourinho. “When a rich guy who has already had a phenomenal career wants holidays, he doesn’t come to play in England. It’s the most difficult league in the world, so if you come here you want to show what you can do. That’s what he did. It’s not just about goals. It’s about leadership and motivation, and I’m so happy with what he’s done. I knew his character and, at his age, he’s a character. A personality. Because he has the passion to play.”

He had the kind of supply-line here, largely from Pogba, for which Christian Benteke was pining at the other end of the pitch. The Frenchman’s understanding with Ibrahimovic could yet be key to United mounting that assault on the top four – they are six points shy of Manchester City at present – and the manner in which Mourinho attempted to envelope the Swede in a bear hug at the final whistle was indicative of that much. The manager was not inclined to hoist up the 35-year-old as his “best” signing but, even on a massive weekly wage, he can feel like a bargain when he conjures definitive moments such as these.

Facebook Twitter Pinterest Paul Pogba opens the scoring moments before the half-time whistle. Photograph: Christopher Lee/Getty Images

Ibrahimovic also had a hand in United’s opener, shipped in stoppage time at the end of the first half just as Palace had dared to believe their industry and endeavour might see them to the break unscathed.

Juan Mata’s free-kick was chested on to his own arm by Ibrahimovic for Pogba, standing marginally offside, to poke beyond Hennessey from close range. The hosts, their shape having been established to stifle rather than scintillate, were momentarily incensed before slumping back to the dressing-room as if resigned to their fate.

Their complaints that Marcos Rojo had received only a yellow for his latest two-footed lunge, this time on Wilfried Zaha, also simmered. Alan Pardew did well to reinvigorate them thereafter before his team benefited from their own dose of fortune. The equaliser was slickly constructed, the hosts more urgent and threatening as they chased parity. David de Gea had already done wonderfully well to deny James McArthur from distance, the Spaniard’s save stunning as he stretched out a right hand in mid-air to turn the effort round the post. Yet the Scot found life rather easier from closer in.

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United were dozing, their rearguard suddenly ragged, as Damien Delaney provided the cutest of flicks round Phil Jones for McArthur, momentarily liberated from Pogba, to collect. He scored with glee, with his team-mates swarming in disbelief around a tickled Delaney.

Yet Palace were unable to build on that momentum and, when United were denied a penalty after Joe Ledley’s handball in the area, they rallied.

Mata had a goal disallowed from Rojo’s nod back, television replays subsequently suggesting he was a toe offside at most, before Ibrahimovic found his range. “Even if this game finished 1-1, I’d have the same feeling towards my players,” said Mourinho. “The performances have been good for a long time, so the players deserve this: happiness at home, and happiness away.”

They are edging back towards the fringes of the title race. Palace, in contrast, are mired in a more desperate struggle at the other end. They could take heart from their effort and commitment, and the reality they had prised apart a stubborn defence, but familiar mistakes crept in.

Just as against City recently, a second-half revival went undone at the last by a lapse of concentration. The decision to fling on Fraizer Campbell for McArthur near the end, disrupting shape yet again, might also be scrutinised. Substitutions are not coming off at present, and there is a whiff of inevitability to their plight. Chelsea visit these parts on Saturday. There is no respite in sight.