Spurs appeared to be heading for an underwhelming draw that would have seen Brighton edge closer to securing their Premier League safety, but Eriksen struck two minutes from time to cruelly deny Chris Hughton's hard-working side.
After a quiet opening, the first half grew into a lively encounter, with Spurs going closest just before the interval when Dele Alli had an effort blocked on the line.
Spurs stepped things up a notch in the second half but looked to have run out of ideas after Toby Alderweireld hit the post, only for Eriksen to eventually find the net late on, taking Mauricio Pochettino's men four points clear of fifth-placed Arsenal..
Precious little occurred during the early exchanges until Victor Wanyama's wild clearance went just over his own goal following a free-kick in the 14th minute.
Spurs livened up soon after and went close to the opener – Lucas Moura collected Eriksen's exquisite pass and played the ball across the face of goal, but Lewis Dunk brilliantly intercepted before Dele Alli could tap in.
Brighton were fortunate again a few moments before half-time – Shane Duffy crucially clearing Alli's close-range effort off the line.
Spurs dominated thereafter, but they struggled to break down Brighton's compact defence – Danny Rose's 25-yard strike testing Mat Ryan, before Alderweireld struck the right-hand post 18 minutes from the end.
Vincent Janssen was introduced for his first Premier League appearance since August 2017 as Spurs ran out of ideas.
But finally their persistence paid off, as Eriksen's left-footed drive found the bottom-right corner from 30 yards to continue Spurs' unblemished start at their new home and keep Brighton looking over their shoulder at Cardiff City in the relegation battle.
What does it mean? Spurs in the driving seat
With all of the candidates for the remaining top-four places dropping points in their last fixtures, it almost seemed as though none of them want Champions League football next season.
Consistency has been hard to come by all for all of them, so a win for Spurs could prove to be massive in the long run, particularly with Chelsea and Manchester United set to face each other at the weekend.
Eriksen elevates Spurs
Match-winner Eriksen had looked like Spurs' most likely route to goal throughout, with the Dane pulling the strings from midfield and going fairly close with a couple of long-range efforts. He eventually found the target and just in time, continuing his fine run of form.
Llorente a peripheral figure
While Fernando Llorente would never be expected to run around and make things happen, he was anonymous even by his standards. He might complain about the service, but he could have made himself more available and he was generally dealt with easily by the excellent Brighton defence.
Key Opta Facts
- Tottenham have won all four of their home games in all competitions since moving into their stadium, scoring eight goals and conceding none.
- Brighton have failed to score in seven consecutive games in all competitions for the first time ever.
- Brighton faced 29 shots in the game, the most they have ever faced in a Premier League game.
- Brighton have lost all 11 of their Premier League away games against 'big six' opponents, conceding 23 goals and scoring just twice.
- Since his Premier League debut in September 2013, Eriksen has scored 21 goals from outside the box in the competition, more than any other player.
Spurs have another two home games on the horizon, as they host West Ham in a London derby on Saturday, before the first leg of their Champions League semi-final against Ajax. Brighton continue their survival battle at home to Newcastle United in four days' time.