José Mourinho’s dark mood was not transformed entirely – Paul Scholes and the so-called “kings of rock and roll” got it in the neck after the game – but the same could not be said of Manchester United’s second-half display at Everton. Clinical, classy and confident; Mourinho’s men welcomed in the new year in a manner that seemed beyond them during their festive slump.

Superb finishes from Anthony Martial and Jesse Lingard brought United a first win in five matches and a return to second place in the Premier League. A 12-point gap remains between themselves and Manchester City but, after a slow-burning start and despite missing several key performers, they imposed their quality and superiority over Sam Allardyce’s ambitionless team. It needs to be a benchmark for the remainder of the campaign or those kings of rock and roll – presumably the “Class of 92” – will be playing the record that so irks the United manager.

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“From the first minute to the 70th we were improving, improving, improving,” said Mourinho. “We controlled the ball, we crossed a lot, the goals were phenomenal, Juan Mata’s shot hit the post and there was an amazing save by the kid [Everton’s Jordan Pickford]. We found a way to play without Romelu [Lukaku] and Zlatan [Ibrahimovic] and we played really well.”

The first half lived down to expectations, reflecting the dour recent form that both teams brought into a contest played on a wet and windy Merseyside evening, but United gradually took command with Paul Pogba to the fore. Mourinho’s new captain almost fashioned a breakthrough when he broke into the Everton area but his low cross eluded several team-mates who were waiting to convert. The midfielder also tested Pickford with a 30-yard drive that the Everton goalkeeper tipped round his post while Martial forced a fine low save from the £30m summer signing.

Allardyce once again deployed his team purely to contain. The end result was a second consecutive defeat and a second home game in succession without an Everton shot on target. Goodison’s patience is wearing thin and Allardyce’s attempts to sign Cenk Tosun from Besiktas have stalled with the Turkish club now demanding more than the £25m agreed in principle last week.

“I presume we will know in the next 24 hours if we are successful or not,” said the Everton manager of the Tosun deal. “We need a bigger goalscoring threat than we have at the moment. Our attacking powers are limited. I knew that before I arrived and that’s why I’ve worked so hard on keeping clean sheets. That’s our main objective, to make sure we pick up more results by not conceding goals and hoping we can score one to win a game. Our ratio of chances created is very limited.”

Mercifully from a United perspective there was improvement after the interval as they built momentum and forced the home side ever deeper. Better movement and distribution was key to their strong start to the second half and Mata twice went close to opening the scoring from distance. The Spain international’s first attempt from 25 yards was pushed over by Pickford. His second, a left-footed drive after cutting inside, flew beyond the goalkeeper but struck a post.

Everton’s reprieve did not last long. The breakthrough had developed an air of inevitability, such was United’s dominance, and was executed with a touch of excellence. At the end of a sweeping counterattack Pogba picked out Martial in more space than he should have been allowed just outside the Everton penalty area. Central, and 20 yards out, the striker took aim for the top-left corner of Pickford’s goal and found his spot perfectly. Martial’s seventh goal of an inconsistent campaign was a fine way to end a barren run.

José Mourinho turns on Paul Scholes after Paul Pogba shines at Everton Read more

Allardyce responded to falling behind by introducing Aaron Lennon and James McCarthy for Yannick Bolasie and Rooney respectively, the latter switch attracting audible derision from the Gwladys Street end. United responded by remaining on the front foot and Pogba twice almost doubled their lead, forcing another good stop from Pickford at close range and just failing to connect cleanly with Martial’s inviting cross moments later. Pogba was a persistent threat roaming in from the left and teed up Lingard for a low shot that Everton’s keeper, yet again, foiled.

In fairness to the Everton manager his double substitution sparked a much-needed reaction from the hosts. Oumar Niasse headed wide when Mason Holgate’s cross found the striker unmarked in front of goal and Everton belatedly exerted pressure on the United defence, but the game was put out of their reach by another supreme finish. Pogba, inevitably, was involved, playing Lingard into space on the left before wheeling away in celebration as the winger cut across a weak challenge by Michael Keane and curled an unstoppable finish into the top corner.

“Boys jump or they don’t jump,” said Mourinho when asked of Lingard’s increasing influence. “It is one thing to be a talent and another to be a very good player. Some players are not capable of that jump, they go from great potential to normal player, but I think Jesse is making that jump.”