They had come to marvel and to party but what the Tottenham hordes truly wanted from the night when their jaw‑dropping new stadium was unveiled was a win: a tonic to re‑energise their faltering push for a top-four finish.

The nervous excitement crackled, particularly during a helter-skelter first half, and there were times when Daniel Levy, the “big boss” as Mauricio Pochettino had called him on Tuesday, might have given his £1bn kingdom for a goal. Further dropped points were not a part of his script.

Then it happened. The honour of marking this venue’s first goal went to Son Heung-min and, as the tension was lanced among the majority of the 59,215 in attendance – oddly, it was not a full house – it was easy to think there could have been few more popular scorers. It was Son’s 17th of the season and one that will stand the test of time.

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Would the stadium boost Spurs or not? There had been no shades of grey. After four defeats and a draw in their previous five Premier League games, they simply had to beat Crystal Palace. Son’s goal soothed them and Christian Eriksen would add a second. To paraphrase Pochettino, this stadium has to have Champions League football. Spurs feel back on track.

Pochettino’s message had been to play the game and not the occasion but it was easier said than done. The club have waited so long for this moment – in Levy’s case, it has been practically the duration of his 18-year chairmanship – and it was always going to be emotional.

Take the opening ceremony, for starters, which featured the students of Gladesmore Community School performing Everybody Dreams. They first produced it in 2012 – one year on from the riots that were sparked in this area – and it is meant to serve as an anthem of hope for the young people of Tottenham.

Facebook Twitter Pinterest Fireworks are seen during the opening ceremony of the Tottenham Hotspur Stadium prior to Spurs’ victory over Crystal Palace. Photograph: Tom Jenkins/The Guardian

When Lanya Matthews, a former Gladesmore student, who appeared on last year’s X Factor, belted out the vocals, she advertised not only her incredible talent but the upscale acoustics inside the bowl. Flags fluttered and there were even fireworks before kick-off.

James Tomkins, the Palace defender, described the ceremony as “not ideal”. He added: “It goes on a bit and it’s a bit surreal.” Goodness knows what was going through the minds of the Spurs players. No pressure, then.

It was frenzied at the outset, best summed up by Son winning a corner and then turning to the crowd to whip them up some more. Pochettino’s starting 4-4-2 set-up had a new-build feel, with Dele Alli in a deep central midfield role and Danny Rose at left midfield. Jeffrey Schlupp ran through in the third minute to thrash a shot off target for Palace – a good chance wasted – and, from a Spurs point of view, it was imperative to settle the anxiety.

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Palace have a better record away than at home this season and there were no surprises about how Roy Hodgson set up. He prioritised solidity and keeping the space between the lines to a minimum. His team defended resolutely until Son’s goal. Hodgson complained his players found the pitch a little slippery and he just wished they could have maintained the 0-0 for another 10 minutes or so.

Spurs pressed on to the front foot, adrenaline coursing through their systems, desperate to find the breakthrough. They were too desperate, at times. Witness Jan Vertonghen’s 40-yard shot, which was blocked, after 31 minutes. Harry Kane also grabbed a free-kick on the edge of the area and messed it up; should he have left it for Eriksen?

The home side camped in the Palace half before the interval and they created chances but too often they snatched at them or made the wrong choices. Rose looked for Kane when he ought to have shot. The closest the hosts came in the first half was when Vicente Guaita saved from Eriksen.

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Over in one corner of the lower tier, the Palace fans chanted their songs without pause and there were periods when their voices were the only ones that hung in the chilly night air. The home crowd implored and fretted at various times. Where was the goal that they craved?

They got it on 55 minutes and if Son’s shot from the edge of the area took a helpful deflection off Luka Milivojevic, Spurs were not complaining. Eriksen had started the move when he robbed the Serb. Moments earlier, Michy Batshuayi had bent a shot narrowly wide of Hugo Lloris’s far post but now the occasion was transformed.

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Kane curled over from Alli’s pass and the Spurs striker was central to the second goal. Initially, it appeared that he had been fouled by James McArthur – he had not – and everybody stopped. Eriksen did not and swept home.

Palace pushed, with Lloris denying Patrick van Aanholt and Wilfried Zaha, while the substitute Christian Benteke headed wide in between. It was too little, too late. Guaita would deny another substitute, Lucas Moura, at the very end but, by then, Spurs had what they craved.

• The headline on this story was amended on 4 April 2019 to remove an inappropriate use of the word “christen”.