An end-to-end contest rife with fouls and stoppages was seemingly destined to end level in North London, as Pape Sarr cancelled out a merited Seagulls opener, which arrived via the boot of Pascal Gross from the penalty spot.
However, with six minutes of injury time on the board, the returning Son Heung-min picked out Brennan Johnson at the back stick to spark bedlam in the capital, as Ange Postecoglou's men rose into the top four of the Premier League table.
Following their returns from the Africa Cup of Nations and Asian Cup respectively, Yves Bissouma and Son were named on the Tottenham bench, but Kaoru Mitoma came straight back into the Brighton XI in place of the injured Joao Pedro.
Ex-Arsenal man Danny Welbeck was also recalled to the Seagulls' lineup, and the veteran attacker needed only 40 seconds to test the gloves of Guglielmo Vicario, breaking away down the right and cutting inside before seeing his curler tipped behind by the Italian at full-stretch.
The visitors enjoyed promising spells of possession in an otherwise scrappy opening 10 minutes, in which Tottenham survived a couple of early corners, thanks to James Maddison shielding Vicario from Welbeck after the events of last weekend.
However, Tottenham would make a mess of trying to play out from the back in the 16th minute, and an episode of pinball inside the Spurs box ended with Micky van de Ven treading on Welbeck's foot, leaving Sam Barratt with no choice but to point to the spot.
With 12-yard specialist Pedro absent through injury, Gross assumed penalty responsibilities and coolly sent Vicario the wrong way to propel Brighton into the lead, and the hosts could not argue that their visitors' lead was merited.
Postecoglou's previously tepid side responded well to going behind, but a one-on-one battle between the red-hot Richarlison and Jason Steele in the 22nd minute saw the Brighton goalkeeper make a fine save, before Tariq Lamptey cleared Timo Werner's follow-up strike away from danger.
Only four minutes later, Maddison tried his luck with a curling strike from the edge of the box, only to see his attempt flash a whisker wide of the upright, but Brighton's high press almost paid dividends again in the 29th minute.
After Rodrigo Bentancur lost possession on the edge of the box, the lively Mitoma sprinted into space on the left and attempted an outside-of-the-foot finish - which Vicario was equal to - and a tetchy nature was beginning to become apparent for the frustrated hosts.
Brighton were in a charitable mood in North London, gifting possession away cheaply on a few occasions, but Tottenham could not capitalise before the break; Richarlison rolled a near-post shot wide in the 36th minute, two moments before Steele kept out a tame effort from a tumbling Dejan Kulusevski.
Neither side made any alterations at half time, and the omens were not promising for Tottenham heading into the second 45, as Brighton had gone 31 Premier League games without suffering defeat when leading at half time, winning 25 of them.
Every Tottenham outfield player took up a position in the Brighton half as they sought to snap the Seagulls' golden sequence, and a decent chance arrived for Werner in the 53rd minute, as the German capitalised on a Lamptey slip, burst infield and got his shot away, but a deflection sent it behind for a corner.
Albion dealt with a few set-pieces that Tottenham threw at them, but Spurs finally found the mark in the 61st minute, as Lewis Dunk did well to divert a Sarr cutback onto the post, but the rebound fell kindly for the Senegalese to tap home into an empty net.
Sarr's equaliser brought Tottenham's Premier League goalscoring streak to a remarkable 36 matches, the joint second-longest run in the history of the competition, and only behind Arsenal's 55 from May 2001 to November 2002.
Spurs fans' celebrations did not die down for another couple of minutes, as Postecoglou sent on the returning Son for his first appearance since December - to rapturous applause from the home crowd - but it was Brighton who began to force the issue again with Tottenham at sixes and sevens.
Two golden chances for the Seagulls came and went in the 76th and 78th minute, as Ansu Fati dragged a shot wide of the far post from a Mitoma cutback before Van de Ven took one where it hurts to deny Buonanotte, but the Seagulls were carving through Spurs like a knife through butter.
Postecoglou's men soon regained a measure of control, and just as the contest appeared set to end in a share of the spoils, a last-gasp Spurs breakaway saw Son pick out Johnson at the back post, and the Welshman could not miss from close range.
On account of their fifth Premier League home win on the trot, Spurs have risen above Aston Villa into the Champions League spots, while Brighton remain eighth, having missed the chance to jump into the European places.
The visit of Wolverhampton Wanderers is next up for Tottenham on February 17, one day before Brighton head to relegation-battling Sheffield United.