Everton burned with a sense of injustice over the record 10-point deduction that has revived relegation fears just when it seemed Sean Dyche’s side had left them behind. Manchester United performed with cool heads and cold intent instead, and savoured the biggest win of their improving season as a result.

United’s previous seven league wins this season had all been by a single‑goal margin but here, against an Everton team reeling from the heaviest sporting sanction in Premier League history, an ultimately comfortable victory was built on character plus the clinical touch that their opponents lack.

Related: Boos can’t lift blues but Everton fans’ spirit of defiance can rouse team | Jonathan Wilson

A stupendous overhead kick from Alejandro Garnacho set Erik ten Hag’s team on their way to an impressive win in which the 18-year-old Kobbie Mainoo excelled on his full debut. A second-half penalty from Marcus Rashford proved pivotal in taking the game away from Everton. Anthony Martial provided the gloss with his first goal of the season late on.

Dyche’s team created a host of good chances – they had 24 attempts on goal compared to United’s nine – and adapted well to the unique circumstances that have enveloped the club. But finishing deserted them yet again at Goodison Park. Everton are five points from safety and cannot allow themselves to become demoralised by a punishment not of their players’ making.

“The message to them is, we can cry and worry about it and say it is unjust, and I think the whole of football thinks it is unjust,” the Everton manager said. “Or we get on with it. We can’t guarantee the appeal, only what we can do about it each week on the pitch.”

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Everton protests against the Premier League were well funded, with more than £40,000 raised for the various banners and 38,000 pink cards that filled Goodison Park, impressively coordinated and executed en masse. There was a wild atmosphere inside the old ground with boos starting as soon as two men stepped on to the pitch carrying Premier League signage before kick-off.

But what an angry crowd and a fired‑up team could not legislate for was an early moment of sheer brilliance from Garnacho. His wondrous overhead kick drew the sting from Everton’s ire, temporarily, and provided an emphatic reminder of the individual talent at Ten Hag’s disposal. For all the angst that surrounds United’s season they are now the league’s in-form team since the beginning of October with five wins from six matches and 15 points. Confidence is one thing Garnacho does not lack, as he confirmed after only 136 seconds.

Everton were exposed by a cross‑field pass from Victor Lindelöf out to Rashford on the right. It would not be the only occasion. Rashford released Diogo Dalot to the by-line and, though his deep cross was sailing away from the danger zone, Garnacho read its flight to perfection. Taking a step back, and turning away from goal, the teenager launched himself into the air to meet Dalot’s delivery with an unstoppable overhead kick that flew into the top corner of Jordan Pickford’s goal with the Everton goalkeeper well beaten. The contender for goal of the season was reminiscent of Wayne Rooney’s spectacular winner for United against Manchester City in 2011. It was no surprise to hear United fans reprising their old Rooney chant moments later.

Garnacho’s goal stunned Everton but gradually their composure on the ball improved to match their intensity. The hosts created enough chances to have led by the interval. Dominic Calvert-Lewin met James Garner’s corner with a towering header that he placed too close to André Onana.

The Everton striker forced a better save from the United keeper with a first-time shot and Dwight McNeil was close to converting the rebound only for Mainoo to clear off the line. The 18‑year‑old was hugely impressive on his first Premier League start and demonstrated why Ten Hag had such high hopes for the central midfielder before injury struck in pre‑season. He denied McNeil again with a fine block when the Everton winger found space inside the United area.

Abdoulaye Doucouré and Idrissa Gana Gueye, goalscorers in the win at Crystal Palace before the international break, were both guilty of glaring misses as Everton increased the pressure before half-time. Goodison’s anger turned towards the referee, John Brooks, after a series of inconsistent decisions, including booking Doucouré for dissent when asking why Garnacho was not cautioned for kicking the ball away.

Everton’s sense of grievance deepened when Brooks awarded United a penalty after a pitch‑side review. The referee initially booked Martial for diving over Ashley Young’s outstretched right foot as he darted into the area. VAR advised Brooks to take a second look and he deemed Martial to have been tripped by the veteran defender. Bruno Fernandes showed a captain’s touch by giving the penalty to Rashford in a bid to boost the striker’s confidence. He duly smashed only his second goal of the season into the top corner.

Martial wrapped up victory at the end of a flowing United move instigated by the substitute Facundo Pellistri. Fernandes dissected the home defence for the forward to lift a nonchalant finish over Pickford and claim his ninth goal in 17 appearances against Everton. He is not the only one whom Everton believe has it in for them.