This was as entertaining a Manchester United display as there has been under Ole Gunnar Solskjær. Midway through the second half the manager was regaled with the song that pleads not to “take my Solskjær away” in recognition of the verve and vibrancy on show.

He was thrilled. “Our best performance of the season, you can go back to Chelsea [4-0] but today the reaction after they scored was fantastic,” the Norwegian said. “Sometimes this season when you get one up how we didn’t [go on] end up five, six, seven, we don’t know but today was exhilarating, entertaining and great to see the boys enjoy themselves.”

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There may have been a worrying weakness under the high ball and regarding United’s ruthlessness but, really, this was a convincing exhibition of the Norwegian’s blueprint for his developing side. It was also a memorable day for the left-back Brandon Williams, who was excellent on his full Premier League debut. Of the 19-year-old, Solskjær said: “He’s making it very hard for me to leave him out.”

From the kick-off United were immediately where their manager wants them: on the front foot, with Marcus Rashford, Daniel James and Andreas Pereira bossing proceedings.

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When James raced down his wing the cross that followed came close to landing on Rashford’s head. A corner was claimed, Pereira delivered and Scott McTominay nearly sneaked in from a left-hand position.

This pace of thought and execution would dizzy the Seagulls until the end. Rashford had one of those days when he was close to unplayable, despite a glaring second-half miss. When Pereira fed him on the left the No 10 flashed infield before his shot was saved to Mathew Ryan’s left.

Soon after United did find the goal. Anthony Martial passed to Pereira and he drove at Brighton. After too many stepovers he seemed to have lost momentum only for the unfortunate Dale Stephens to hit the ball to Martial. The Frenchman’s first touch was clumsy but he still played Pereira in: the latter’s effort might not have troubled Ryan but Stephens’s deflection this time turned the ball into the net.

Facebook Twitter Pinterest Lewis Dunk, second left, hits back with a headed goal for Brighton at Old Trafford. Photograph: Matt West/BPI/REX/Shutterstock

Two minutes later United had a second. Harry Maguire and Lewis Dunk fought for the ball and when it dropped Davy Pröpper, under duress from McTominay, put the ball into his own net. VAR ruled Maguire had not impeded Dunk and United were coasting.

United now needed to ensure they remained in control. Instead a Maguire error near halfway led to a Brighton free-kick along the right. Leandro Trossard pinged this in, no red shirt cleared and Dunk might have finished.

United’s defence was again poor in the air when Trossard hit another dead ball over from the right as the interval neared. Aaron Connolly was free and, like Dunk, should have scored.

Fred has lately started to perform like his £55m price suggests he should. “You get confidence from playing games,” said Solskjær. A pass he flipped from within a crowd of players near his area was guided into James superbly and after the Welshman sprinted forward and crossed only Dunk’s clearing header denied Rashford a chance to make it 3-0.

More of the same with tighter defending might have been Solskjær’s orders for the second half. Graham Potter acted by removing Martín Montoya and Connolly for Solly March and Glenn Murray. United’s intent was illustrated by a Martial swivel and shot, then a James burst later. When Brighton tried to play out from the back the United front three were a rapid-pressing unit that allowed them scant time.

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The sense was of United being hungrier than their opponents. Williams followed a yellow card for a high challenge on Steven Alzate by hunting down a throw-in. Brighton’s only hope was if the home team might implode.

On 64 minutes there was a glimmer. Fred’s fine performance was marred by a fluffed clearance that led to a corner on the left. Pascal Gross swung this in and, again, United were deficient in the air, Pereira losing Dunk, who powered home.

It did not stay 2-1 for long. Fred redeemed himself with a precise 30-yard pass that put Martial through. He turned the ball to Rashford and the striker drilled past Ryan off the bar.

Old Trafford was jubilant and within seconds Rashford should have had a second. James’s speed took him clear down the right, he chose the correct option in finding Rashford, yet from three yards and with Ryan stranded, the 22-year-old missed.

It did not deter him or his teammates, though. Williams saw his attempt saved by Ryan, then the keeper did the same with a James volley and, at the close, Rashford again might have made it 4-1.

This had been impressive from United, though McTominay limping off in added time was a concern. “It’s an ankle – I’ve had one and it can be eight weeks, then again it could be two,” said Solskjær, who said the Scot is to have a scan on Monday so is unlikely to report for international duty.