It was on this day last year that Brighton ensured their promotion from the Championship. On Tuesday night at the Amex Stadium they took a small step towards retaining their Premier League status for another season.

The fiendish nature of their run-in has been well-documented and Chris Hughton’s team must still face the Manchester clubs, Liverpool and Burnley in their final matches. They needed something, anything, to allow them to breathe a little easily after a worrying run of one point from an available 15. This was it.

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The horror of Saturday’s 3-2 defeat at Crystal Palace was forgotten as Brighton put their bodies on the line to earn precious reward. The roar from the home crowd at the full-time whistle told its own story. Brighton are eight points clear of third-from-bottom Southampton, although they have played a game more.

Tottenham have a bigger match round the corner in the shape of Saturday’s FA Cup semi-final against Manchester United and Mauricio Pochettino appeared to have one eye on it with his team selection. He made six changes from Saturday’s home defeat by Manchester City and omitted Davinson Sánchez and Dele Alli from the squad entirely. He gave Toby Alderweireld his first Premier League action since 28 October and the centre-half was not overly extended.

However, Pochettino made the point yet again that the league was the priority. The personnel changes, he said, were purely down to fatigue from the City game. “If we win the FA Cup, we are not going to play Champions League,” Pochettino said. “You only do that if you finish in the top four. Today was the most important game.”

For Tottenham it felt like points dropped. Pochettino was entitled to say that his team had “dominated” the game in terms of possession and territory but he was also on the money when he lamented a “lack of aggression” in the final third. They were unable to create sufficient clear-cut chances.

Harry Kane put Spurs in front with his 26th goal of the Premier League season – his Golden Boot rival, Mohamed Salah of Liverpool, has 30 – but Brighton showed their strength of character with an instant riposte through Pascal Gross’s penalty. Hughton had given him the responsibility after a couple of penalty misses this season by Glenn Murray.

Facebook Twitter Pinterest Pascal Gross beats Hugo Lloris from the spot after replacing Glenn Murray as Brighton’s penalty taker. Photograph: Tottenham Hotspur FC/(Credit too long, see caption)

Tottenham’s lead over fifth-placed Chelsea could be cut to five points with four matches to play when their London rivals go to Burnley on Thursday. But theirs remains a position of strength. Three of their final four matches are at Wembley – against Watford, Newcastle and Leicester – and the other one is a trip to West Brom.

Pochettino’s team sought to impose their pressing game and they sparked danger on a number of occasions when they forced errors from Brighton high up the pitch. Gross was guilty of the stray pass that set in motion the move for Kane’s goal at the beginning of the second half.

He put Gaëtan Bong in trouble, the left-back was tackled by Victor Wanyama and, when the ball broke, Son Heung-min tried to run round Lewis Dunk on the byline. Son did not look to have the room but he benefited from the spin of the ball, which remained on the right side of the line, and the alarm bells sounded when Kane swooped. He crashed home from close range.

Brighton’s response was impressive. José Izquierdo got away from Serge Aurier inside the box following Murray’s touch and the Tottenham right-back’s attempt to rectify the situation was clumsy. Izquierdo felt the contact and went down. Gross’s penalty was too powerful for Hugo Lloris.

The first half had been end-to-end without too many thrills in front of goal. Son, who menaced Bruno, the Brighton right-back and captain, had the clearest chance in the third minute of stoppage-time. Taking a flick from Kane, he eked out a yard of space before shooting for the bottom corner. Mathew Ryan thrust out a hand to save smartly.

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Set pieces had seemed the likeliest route to the breakthrough. The tension inside the ground was palpable when Christian Eriksen and Kane stood over free-kicks on the edge of the Brighton area on 11 and 44 minutes respectively, but neither could convert. The awards had followed loose passes from Beram Kayal and Anthony Knockaert.

At the other end Dunk rose to direct a towering header at goal from Gross’s 19th minute corner and Anthony Knockaert almost applied the decisive touch in front of Lloris. Knockaert was a willing and pacy outlet and he worked Lloris with a deflected shot while Murray could not muster sufficient power in his flick after slick work from Gross. Ryan also had to be alert to tip over a long ranger from Lucas Moura.

Tottenham pushed for the winner in the second half, with Pochettino introducing Mousa Dembélé and Erik Lamela, but Brighton’s resolve was fierce. Their support endured a few flutters, not least when Eriksen fizzed in a cross-cum-shot and Shane Duffy diverted the ball inches past the far post, while Lamela was denied by Ryan. Hughton’s battlers had done enough.