Brighton have enjoyed plenty of giddy highs since their restoration to the top division last summer but this was a victory to cap them all. By securing a first win over Manchester United in 36 years Chris Hughton’s team are safe. The wave of relief that swept round the Amex at the final whistle swiftly turned to raucous delight. There will be top-flight football in Sussex by the sea for another year.

This was a glorious way to achieve a season’s objective, a success achieved as Pascal Gross’s header crept exactly 28.3mm over the goal-line before Marcos Rojo could hook the effort away, and one to be savoured through the delighted din of the players’ post-match lap of appreciation.

Gross was outstanding, as he has been for much of his first season in England since joining for £3m after Ingolstadt slipped out of the Bundesliga. The German’s determination to reach José Izquierdo’s centre, which had flicked off David de Gea’s glove into a muddle of bodies off the far post, summed up the home side’s urgent desire to secure safety, even if their goal celebrations were briefly delayed until the referee’s watch had buzzed.

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Albion’s run-in had always looked daunting, with trips to the Premier League champions and Champions League finalists to come in the final week. Yet by winning for the first time since early March and discomforting United all night, they have quelled fears of a late sting in the season’s tail.

“It’s a relief because I felt we’ve deserved to stay in this league for our season’s work,” said Hughton. “If we’d lost today and the next two and somehow gone down, it would have been a real feeling of injustice. Normally when you win this type of game it’s because you’ve played at a good level and maybe your keeper has had to make some good saves or they’ve missed some chances. But United didn’t have a clear-cut chance in the 90 minutes. We were good value for the win.”

That was an understatement. Brighton’s attacking approach play had been more assured and incisive all night, led by Izquierdo and Anthony Knockaert, who tends to rouse himself for occasions such as these. The hosts’ back-line was obdurate and organised, their midfield industrious and energetic and neither of United’s centre-halves ever appeared at ease in trying to combat the splendidly awkward Glenn Murray. De Gea’s stunning first-half save denied the striker from distance. Izquierdo would be thwarted in similar fashion before José Mourinho could haul his players back into the dressing-room for a dressing-down.

Facebook Twitter Pinterest Brighton players celebrate Gross’s goal, with goalkeeper Mat Ryan running the length of the pitch to join in. Photograph: Mike Hewitt/Getty Images

This is the first time United have been beaten at the three promoted teams in a top-flight season and, while they are still likely to finish second, few of those offered chances to impress will, on this evidence, now merit inclusion in the FA Cup final line-up. The Portuguese was a picture of disgust through most of the first half, eventually retreating from his technical area as if to distance himself from such a mess of a performance. Where Albion were urgent and energetic, the visitors were horribly slack.

Simple passes were repeatedly guided out of play, team-mates delivering blindly and misreading colleagues’ runs, their wavelengths forever scrambled. Sloppiness infected the visitors’ approach, with Marcus Rashford and Anthony Martial, players for whom there has been a clamour for greater involvement, either too anxious to impress or too rusty to do themselves justice. In the end the injured Alexis Sánchez and Romelu Lukaku actually emerged with their own reputations enhanced in absentia. Both will hope to be fit for the game at Wembley against Chelsea.

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United’s best opportunity was spurned as the final whistle approached, Rashford flicking a return pass inside for the substitute Jesse Lingard just inside the penalty area, only for the former Brighton loanee to skew his shot wide as Shane Duffy dived in to challenge.

Mourinho had made a beeline for Hughton on the touchline as soon as the chance was missed, offering him a hug of congratulations. The United manager had seen all this coming, as he admitted post-match, but had been helpless to prevent the reverse.

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Brighton boasted all the motivation and, in the end, could lose themselves in delirious huddles as the ecstatic home support itched to invade the playing surface to join them. This was their night.