For Manchester United fans, it is the hope that kills them. The hope Ole Gunnar Solskjær can find the answers, that the flickers of promise from his tenure can morph into meaningful momentum, that the romance inherent in his appointment can somehow override the problems and the drift at the top of the club.

This was a game in which Liverpool’s superiority was so pronounced for most of the first half and the early part of the second it would have been no surprise had they led by five or six. The intensity of their football coupled with the surgical nature of their incisions were enough to take the breath. It certainly seemed to take that of United and it felt like the latest reality check for Solskjær and his players.

The hope persisted as United somehow emerged from the storm to play a bit of front-foot football. Anthony Martial even missed an excellent chance for an improbable equaliser. United fought until the end.

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And yet at the very end, after United had loaded men into the Liverpool area for an all-or-nothing corner, there was Mohamed Salah racing on to Alisson’s clearance, holding off Daniel James and finally giving Liverpool the breathing space they had craved. Alisson ran the length of the pitch to celebrate with a knee-slide in front of Salah.

The Kop bellowed about winning the Premier League, about how people would now believe them and it was difficult to see who might not. Liverpool’s invincible streak goes on – they are unbeaten in 39 league games, the fourth best run in English top-flight history, and they are 16 points clear of second-placed Manchester City with a game in hand. This was their seventh consecutive clean sheet in the competition. A first title in 30 years is all but theirs.

For United, it was another example of their best efforts being inadequate. With Chelsea having lost at Newcastle on Saturday, they had seen an opportunity to close the gap to the top four. They failed. Yes, they avoided a hammering and salvaged some pride but they cannot be oblivious to the bigger picture, one which shows the chasm that has developed between themselves and their fiercest rivals.

Solskjær had reassured himself that United were the only team to have taken anything from Liverpool in the league this season and he started with the 3-4-1-2 system he had used to good effect in the 1-1 draw at Old Trafford last October. United settled the quicker but this team of Jürgen Klopp’s are not easily knocked from their stride. They have tended to find the answers, the means to take control and they did so on 14 minutes following a corner that gravely undermined Solskjær’s plans.

It is always galling to concede from a set piece and even more so when it involves a breakdown in the marking. Why was Brandon Williams, who stands at 5ft 6in, assigned the task of tracking Virgil van Dijk, one of the most dominant aerial forces in the game? With Harry Maguire blocked off by Joe Gomez, Van Dijk rose to head home Trent Alexander-Arnold’s delivery.

Facebook Twitter Pinterest Virgil van Dijk heads home Liverpool’s first goal from a corner. Photograph: Simon Stacpoole/Offside via Getty Images

It was as if a switch had been flicked. Liverpool surged, the energy crackled. They squeezed United, suffocated them and came to camp inside their half for much of the remainder of the first half. It was all United could do to enjoy any peace on the ball. Liverpool were too quick, too tenacious and, but for a VAR overrule, they would have been 2-0 up in the 24th minute.

Van Dijk went up with David de Gea and there was contact, so much so that United temporarily stopped, expecting the whistle. It did not come. Sadio Mané won the ball back from Victor Lindelöf and Roberto Firmino curled into the far corner. Cue United fury and, after review, an acknowledgement that Van Dijk had fouled De Gea. It was a tight call.

Moments earlier, Luke Shaw had denied Mané with a saving challenge after Firmino’s cross had broken off Fred and Liverpool, the scent of blood in their nostrils, poured forward for more. Firmino could not finish from Salah’s cross and Liverpool had another goal ruled out, this time for offside, after Gini Wijnaldum was deemed to have been fractionally ahead of the last man before he steered home from Alex Oxlade-Chamberlain’s pass.

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De Gea would be forced into a one-on-one block with his legs to keep out Mané and United’s only real moment of first-half note came when Aaron Wan-Bissaka, stealing into space, prodded Martial’s cross across goal. Andreas Pereira could not stretch to apply a decisive touch at the far post.

Liverpool’s remorselessness has been a feature of their fabulous run and they returned their foot to United’s throat on the second-half restart. Salah somehow fluffed his lines from close-range after Andy Robertson’s cross and a Shaw misjudgment, while Jordan Henderson banged a shot against the outside of the post.

How was it only 1-0? It felt like a trick of the mind and yet, while the margin remained slender, United retained hope. They told themselves it might take only one chance. And, after Fred had shot wide, they created the gilt-edged one, Martial swapping passes with Pereira to set up the shot inside the box. He slashed high.

Mané prodded wide at the other end and, with United sensing a reprieve, Martial and Fred had shots on goal. Liverpool, though, would not relinquish what they had.