It was difficult to imagine a more perfect afternoon for Arne Slot – or a more harrowing one for Erik ten Hag who, just three games into the Premier League season, is back in familiar territory; the vultures circling, his credentials as the Manchester United manager under yet more scrutiny.

Slot had won his first two games in charge of Liverpool – against Ipswich and Brentford – but this was supposed to be an acid test. It was not, United so obliging, their first-half woes epitomised by a terrible performance from Casemiro. Things did not get any better thereafter, the only consolation being that they avoided a real pasting, one to rival the 7-0 at Anfield from two seasons ago. Liverpool had the chances to rack up a similar number of goals.

Related: Manchester United 0-3 Liverpool: Premier League – live reaction

A manager can beat only what is in front of him and Slot and his players did the job with a flourish. Their superiority in every area was pronounced and when Luis Díaz scored his second goal for 2-0 at the end of the first half, it became nothing more than a question of the eventual margin of victory.

They contented themselves with one more from Mohamed Salah – the perennial thorn in United’s side – and Slot could reflect on more than a fluid attacking performance. His team were remorseless without the ball and it was a third clean sheet in three games for them. At the end of it all, the message was clear: Slot intends to be in the title shake-up.

Old Trafford was half empty by full-time, those who remained too stunned to jeer. The TV cameras had made the obligatory cutaways to a grim-faced Sir Jim Ratcliffe in the stands and United’s minority owner has plenty to ponder. As does everyone connected to the club.

It was loud and raw at the outset, the United fans bringing the fire, as Ten Hag had demanded, but it was not long before those who had travelled from Liverpool were making themselves heard. And enjoying themselves. It was impossible to ignore the inflatable “seven” and “zero” that some of them had brought along.

Liverpool thought they had scored early only for a VAR intervention to rule out Trent Alexander-Arnold’s finish; Salah was offside when he got a touch on Díaz’s pull-back. The move had been ignited by Ryan Gravenberch’s jet-heeled burst from midfield; United’s defence was sliced open – a sign of things to come.

Liverpool did not let the disappointment affect them. They teemed with intensity, squeezing high, nipping in front to win possession. They took a grip on midfield, where United were extremely open. It was easy to worry from an early juncture about Casemiro not being quick enough on the ball. Or without it. Sadly for United’s holding midfielder, the first half turned into an ordeal for him.

The breakthrough followed a misplaced Casemiro pass and a lightning fast Liverpool counter; it was Slot’s blueprint throughout. The outstanding Gravenberch found Salah and when he crossed, Liverpool had two men over at the far post. At least United did not allow them three, as they had done at Brighton the previous weekend when they conceded the last-gasp winner. Dominik Szoboszlai could not reach Salah’s cross. Díaz could.

Casemiro had followed through high and dangerously on Alexis Mac Allister in the 11th minute and was fortunate to escape a booking; it was the only break he got. There were nearly too many awful moments from him to mention, including losing his balance and the ball by the sideline, heavy touches and lots of loose passing.

Ten Hag sent Toby Collyer out to warm up at the end of the first half – the 20-year-old replaced Casemiro for the second period– and, by then, it was 2-0. When Casemiro dithered on the ball, Díaz robbed him and Liverpool were away again. They worked the ball out to Salah, who came inside for Díaz. The finish was low and lethal.

Liverpool might have had more before half-time. Szoboszlai could not get a clean connection on an Andy Robertson cross while the full debutant Matthijs de Ligt made a one-on-one challenge to thwart Diogo Jota. United’s only first-half flicker was a Noussair Mazraoui shot that Alisson turned away.

Liverpool were in the mood to pile on the pain. The dreaded no-go zone between United’s defence and midfield was back and whenever Liverpool pushed into it, especially on transitions, the sirens sounded.

The third goal came after Mac Allister robbed Kobbie Mainoo and, yet again, Liverpool could scent blood, United’s resistance absent. Szoboszlai played in Salah to score and the visitors might have added two more immediately, United looking vulnerable as they tend to do after conceding. Lisandro Martínez gave the ball away and was lucky that Salah lifted high while the Liverpool forward also saw a curling shot deflect past the far post.

United stared at complete humiliation and Old Trafford was an angsty place, boos greeting Ten Hag’s substitution of Alejandro Garnacho for Amad Diallo. It felt as though the fans wanted him to withdraw the ineffective Marcus Rashford. Frankly, Ten Hag could have hooked anybody.

United did have chances in the second half. Joshua Zirkzee – another full debutant – went close three times, Alisson making a couple of decent saves, and they looked more secure towards the end after Harry Maguire came on for De Ligt. More revealing, though, was Szoboszlai’s miss on 79 minutes when he simply tried to be too clever. It was little wonder, because it had been too easy for his team.

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