Marcus Rashford decorated his 200th Manchester United appearance with a two-goal display of menace that ensured victory over a hapless Norwich. The forward was taken off just before the hour and headed for the changing room.

Ole Gunnar Solskjær said: “What an achievement to get to 200 games at his age. He is absolutely top-class to work with. A great kid, wants to learn, improve, knows to keep his feet on the ground and today he’s carrying a few knocks but no chance he’s going to say to me before the game he doesn’t want to play.”

Solskjær is unsure whether Rashford will be able to face Wolves in Wednesday’s FA Cup third-round replay. “I don’t know but if he’s ready he’s played many games so [we] might have to look at how we can manage him,” the manager said.

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Midway through the second half the singing section were heard chanting against Ed Woodward, United’s executive vice-chairman, and owners, the Glazers.

Solskjær said: “I’m not sure if the players will get it but I noticed. As a club we’ve got to stick together, we’ve got to be united, we are a family. I can only say from when I’ve been here I’ve been backed by the owners, I’ve been backed by Ed and they’re supporting me.

“We are in all competitions. We are still in the Carabao Cup, FA Cup, we’re fifth in the league, still challenging, we’ve improved the position from last season, we’ve got the Europa League.

“They’ve [the fans] just got to believe me when I say I feel we are doing loads of good things behind the scenes, we are going in the right direction.

“See the group today – the attitude, the work-rate, that’s the core of the group that’s going to go forward.”

Harry Maguire was a headline inclusion – the captain recovering quickly from a hip problem – as United were bright throughout. The key was pace: of thought and execution.

United’s opener was impressive. If Juan Mata’s sluggish speed means he has become a squad player his vision is not in doubt. So it was that he could send a curving ball that sliced open the defence and allowed Rashford to hit an aerial finish past Tim Krul.

United had clicked into a higher gear. The excellent Brandon Williams roved inside, fed Fred and the midfielder took aim. A Rashford sprint along the right ended with a cross that splayed Norwich. Later, he sprayed a 30-yard diagonal from the other wing straight into Aaron Wan-Bissaka’s path.

On the touchline Mike Phelan, Solskjær’s assistant, was a head-in-hands embodiment of United’s frustration they had still not doubled their advantage.

Without David de Gea they would have conceded an equaliser just before the break, too. When Norwich broke quickly Emiliano Buendía was allowed to dance across the face of the area and feed Todd Cantwell and only an outstanding save sustained United’s lead.

They heeded the warning and attacked from the start of the second half and were rewarded almost instantly. Maguire fed Rashford and he played the ball in behind to the galloping Williams. The 19-year-old’s pace took him past Krul who upended him and the referee, Anthony Taylor, awarded the penalty.

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Rashford smashed the ball home and United were soon poised to go 3-0 ahead. This was courtesy of another deft Mata ball – from a short corner – that had Anthony Martial leaping between Grant Hanley and Alexander Tettey to head in.

Williams should have made it four as Norwich fell apart. Fred chipped a pass to Martial along the right and he relayed the ball to Andreas Pereira. He flipped a delivery across goal and the left-back’s 50-yard run finished with him somehow missing from mere inches.

After Daniel James replaced Rashford, United hunted for more goals to boost their confidence. Mason Greenwood – on for Pereira – delivered, beating Krul with an impressive 20-yard finish.

Daniel Farke, whose side remain bottom, said: “It is not easy for the belief or the confidence. But it is important to be realistic. It was not a season-defining game for us.”