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Christian Eriksen's stunning late winner finally ended Brighton's resistance to boost Tottenham's hopes of a top-four finish in the Premier League.
Brighton were on course to gain a point in their battle to avoid relegation before the Denmark playmaker - Spurs' most effective attacking player throughout - shot low into the corner from 25 yards in the 88th minute.
Spurs defender Toby Alderweireld had earlier hit the post while his team-mates Lucas Moura and Dele Alli both had efforts cleared off the goalline.
Brighton, without a goal in seven matches, were restricted to counter attacks and set pieces, with the impressive central defensive pairing of Lewis Dunk and Shane Duffy both heading off target.
Third-placed Tottenham are now three points ahead of Chelsea and four clear of Arsenal in fifth, although the Gunners have a game in hand.
Brighton - who have to play both Arsenal and title-chasing Manchester City - remain 17th, three points clear of third-bottom Cardiff with three matches of the season remaining.
Before the match Spurs boss Mauricio Pochettino described the game as a "must win" so will be relieved his side eventually converted their 78% possession into a decisive moment with their 29th effort at goal.
It was always likely to be Eriksen who unlocked Brighton's well-organised defence given he had created his side's best chances.
His early cross was headed over by Belgium defender Jan Vertonghen then minutes later England's Alli narrowly failed to get a touch on another Eriksen delivery.
Brazil forward Moura was also played in by Eriksen and although his shot evaded Seagulls keeper Mat Ryan, it was cleared off the line by Dunk - whose centre-back partner Duffy denied Alli in similar fashion soon after.
Spurs continued to create chances in the second half with Eriksen and Son Heung-min both shooting over before Danny Rose forced a fine one-handed save from Ryan.
Alderweireld's shot on the turn from the edge of the penalty area hit the inside of the post and bounced out and Spurs were so desperate for a goal that they turned to striker Vincent Janssen for his first Spurs appearance since August 2017.
There looked to be minimal danger when Alli slid a pass to Eriksen 40 yards out but his fine strike from outside the area defeated Ryan to earn his side three points.
Brighton face a battle to extend their run in the top flight for a third consecutive year, especially as their final two matches are away at Arsenal before ending the season at home to Manchester City.
Tottenham had not been involved in a goalless draw in their past 67 Premier League games but Dunk and Duffy were so solid for the visitors that the run looked likely to end.
Brighton had conceded seven goals in two games before a goalless draw at Wolves on Saturday and were only two minutes away from another clean sheet thanks to their resilient defending.
But the problems for Chris Hughton's side lie at the other end of the field as they have now not scored in the Premier League since their 2-1 win at Crystal Palace on 9 March.
Hughton latest attempt to find a goal resulted in top goalscorer Glenn Murray being named a substitute in one of six changes to his starting line-up.
Brighton were perhaps fortunate that Florin Andone was not dismissed after he was booked in the 35th minute for a foul on Rose and then within 60 seconds fouling Kieran Trippier.
Referee Christopher Kavanagh opted against a second yellow but the Seagulls' luck ran out with only two minutes remaining.
Tottenham manager Mauricio Pochettino, speaking to BBC Sport: "It was a difficult game, we knew how difficult it would be, how tough it is to break down the opposition.
"Brighton were a really brave opponent. The most important thing is we believed, didn't give up and tried different ways to score.
"It is three very important points and to be in a good position in the table. The team are doing a fantastic effort after tough games against Manchester City.
"The team are not as fresh as we wanted, not just legs, but minds, so we have to congratulate the players. I'm so proud of them."
Brighton manager Chris Hughton, speaking to BBC Sport: "There are some games where you think the other team are going to open you up and the longer the game went on they were pushing bodies forward but I thought we were going to get a point.
"We had opportunities to manage the game better at the end and those are the details that are crucial against a team of the quality of Tottenham. The changing room at the moment is very down because of the manner of the defeat.
"We've got three games and we have to make sure we get enough points to secure our status in this division. The pressure comes with the territory and we'll have to deal with it."
On going seven games without scoring: "We've found it difficult in the opposition half and the final third. What we have done is got back to ourselves in terms of resilience.
"We've never been big goalscorers but in whichever way we can, we need to get it somehow and we have an opportunity at home against Newcastle on Saturday."
