Amid all the excitement surrounding Tottenham’s Champions League semi-final against Ajax it has been possible to forget their basic target for the season remains a top four domestic finish. There was no room for a slip-up against Brighton, no scope for their focus to drop and, on a dramatic night, they got the result that they wanted. Just.

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There were 88 minutes on the clock when Christian Eriksen picked up possession in front of the Brighton penalty area, as he had done throughout the match, probing for the solution. It had eluded him yet this time he found it, arrowing a low drive through the defensive shackles and into the bottom corner.

Like Eriksen, Mauricio Pochettino had struggled to see a way through. The Spurs manager even sent on Vincent Janssen as an 80th-minute substitute; the club’s forgotten striker was given a stirring ovation on his first action of a bizarre season. But thanks to Eriksen’s flash of inspiration, Spurs remain on course.

It is a curiosity that they have lost as many league games this season – 11 – as they did in the previous two combined. Yet they have drawn only once and have frequently been rewarded for their indomitable spirit. Their run-in features two home games out of three – against West Ham and Everton – and their record at their stadium remains unblemished. It shows four wins from four matches in all competitions and no goals conceded. Their other fixture comes at Bournemouth.

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Chris Hughton has been in the game for long enough to know how cruel it can be and this was the latest reminder. At full time, he marched over to the Brighton supporters, hands held high in applause; the picture of defiance. On the inside, he was devastated.

Hughton must go back to the 2-1 win at Crystal Palace on 9 March for Brighton’s last league goals; they have gone 660 minutes without scoring. But this looked like being a match when what they did at the back would fire their survival hopes. Lewis Dunk, in particular, was immense. The centre-half sank to his knees when Eriksen’s goal went in and for him and his teammates it added up to a sixth defeat in seven matches.

Brighton had started the day in 17th place, three points clear of Cardiff, who had played one game more, and under no illusions about the size of their task. Their home match against Newcastle on Saturday already felt enormous and how about it now? Brighton finish with a visit to Arsenal and home game against Manchester City and the fear for them is that Cardiff may get something from their games with Fulham (away) and Crystal Palace (home).

Facebook Twitter Pinterest Christian Eriksen lets fly from outside the area. Photograph: Dylan Martinez/Reuters

Brighton’s determination was ferocious. Hughton’s men flooded the space around the Spurs attackers while they put their bodies on the line time and again, none more so than Dunk, who made some colossal interventions.

It was rough and ready at times – witness Jan Vertonghen’s elbow on Florin Andone in the 25th minute, which he levered into his opponent, rather than throwing it. The referee, Christopher Kavanagh, took no action.

Andone himself diced with disaster. Harshly booked for a trip on Danny Rose, as Kavanagh tried to assert his authority, the Brighton striker stamped into a tackle on Kieran Trippier in the 36th minute, missing the ball and catching the Spurs full-back. It looked like more of a yellow card than the one he received but Kavanagh disagreed.

Spurs lacked invention in the first half. Dele Alli took a marvellous touch on a high ball and prodded goalwards only for Shane Duffy to clear off the line, while Vertonghen saw Dunk block a shot at close quarters. It was otherwise heavy going. Brighton could point to a one-man break from Andone that was halted by a slide challenge from Rose.

Zac Efron brought a touch of Hollywood glamour – the actor, who was picked out by the TV cameras, changed into a Spurs shirt for the second half – yet there was frustration around him, particularly at the delaying tactics of the Brighton goalkeeper, Mat Ryan.

Duffy headed at Hugo Lloris from a tight angle on 46 minutes but the pattern was entrenched: Spurs pushing, Brighton resisting. There were lengthy periods in the second half when Lloris was the only player outside of Brighton’s defensive third.

The margins were agonisingly fine. Toby Alderweireld saw a shot hit the inside of the post and roll across goal but Spurs could not force the ball home and they had other chances. Rose’s dipping long-range shot was palmed up in the air and away by Ryan, while Alli, Son Heung-min and Trippier all went close.

Not for the first time, Spurs could be grateful to Eriksen. He has been tipped to depart in the summer when he enters the final year on his contract but losing him does not bear thinking about.

“It is a very special situation,” Pochettino said. “The timing for him or for the club to be agreeing something is maybe different to another player. I hope and I wish Christian can be with us in the future. Christian and us – we are so open to talk and we will see what happens. It is so close, the end of the season, and [there is] a lot of time to talk after.”