Harry Kane gave the visitors the lead early in the second half but after Brighton equalised from the penalty spot through Pascal Gross just two minutes later, the Seagulls were able to hold on to what could prove to be a vital point.
Spurs have extended their advantage over fifth-placed Chelsea to eight points, while Brighton now sit eight points clear of the relegation zone with four matches remaining.
Spurs dominated the opening 15 minutes on the south coast but after failing to create anything of note in the final third, Brighton almost made the visitors pay as Lewis Dunk's header was spilled by Hugo Lloris before the goalkeeper recovered to claim at the second attempt.
Anthony Knockaert then took it upon himself to try his luck from 30 yards, with Lloris reacting well to keep out his deflected effort, before Spurs threatened at the other end when Son Heung-min's strike from an acute angle was saved at the near post by Mathew Ryan.
Brighton continued to press but Kane had been quiet during the first half-hour and the forward appeared to rush his attempt when shooting over from 20 yards.
Lucas Moura's strike moments later was better, with Ryan tipping the Brazilian's 25-yard effort over the bar, but Brighton could have snatched the lead at the other end when Dale Stephens saw a flick prevented from going into the net by a defender and Lloris.
Brighton began to sit back as half time got nearer and Spurs nearly capitalised deep into added-on time when Kane teed up Son inside of the penalty area, but the South Korean's low strike was brilliantly diverted behind by Ryan.
Within three minutes of the restart, however, Spurs were ahead. Son capitalised on a mistake from Gaetan Bong before taking the ball around Ryan and setting up Kane, who powered the ball into the net from eight yards out.
Mauricio Pochettino would have expected his team to build on taking the lead but within 18 seconds, Brighton were gifted a way back into the match when Serge Aurier brought down Jose Izquierdo inside the penalty area and Gross made no mistake from the spot.
Brighton were in the ascendancy after the goal, but Spurs soon swung the tempo of the contest in their favour and Moura should have taken advantage from 12 yards out, only to drag an effort wide of the near post.
Spurs were dominating possession but they were struggling to break down a packed Seagulls backline, who almost contributed to their own downfall when Shane Duffy deflected a cross marginally wide of the far post.
During the closing 10 minutes, Kane dragged a shot well wide before being substituted, while Erik Lamela fired tamely at Ryan after the ball had broken kindly for him inside the area.
Brighton also tried to rally for a late winner but even though Gross's volley cleared the crossbar, manager Chris Hughton will be delighted with a point from the first of five matches against teams sitting in the top seven of the standings.
BRIGHTON & HOVE ALBION XI: Ryan; Bruno, Duffy, Dunk, Bong; Kayal, Stephens; Knockaert, Gross, Izquierdo (March 77'); Murray (Ulloa 74')
TOTTENHAM HOTSPUR XI: Lloris; Aurier, Alderweireld, Vertonghen, Davies; Wanyama, Sissoko (Dembele 74'); Eriksen, Moura (Lamela 74'), Son; Kane (Llorente 85')