This was just a fourth win in all competitions since August for Mauricio Pochettino's side but they made heavy weather of progressing into the quarter-finals as substitute Erik Lamela and top goalscorer Harry Kane struck in the second half to see off their Sky Bet Championship opponents.
With only two league wins all season and no victory since their round three success over Burton, there could have been much trickier visitors to north London than Sami Hyypia's Seagulls.
But, with kick-off delayed by 15 minutes due to gridlock on the streets around the ground, it was Tottenham who struggled to get out of first gear with 10 changes from the side that was beaten here by Newcastle on Sunday.
Despite his complaints about the small pitch at White Hart Lane Pochettino deployed two out-and-out wingers in Andros Townsend and Aaron Lennon - with the duo looking the most likely to make something happen for the nervous hosts in the opening stages.
Club-record signing Lamela was introduced at half-time and needed just nine minutes to open the scoring before Kane, dropped for the weekend loss, added to his Europa League hat-trick of six days ago to seal the tie.
Mark Clattenburg, dropped from Premier League duty for the coming weekend after his indiscretions following Crystal Palace's recent draw at West Brom, was in charge and infuriated Hyypia when he failed to give a penalty to the away side after Kyle Naughton appeared to handle in the box.
In truth Brighton never looked like springing a cup upset and go back to searching for form in their league campaign instead of continuing on in the hope of reaching Wembley.
Kane had an early effort deflected behind for a corner by Lewis Dunk before Andros Townsend worked some space on the right-hand side of the box and fed the ball to skipper Aaron Lennon, whose shot was turned behind by Rohan Ince, with Federico Fazio heading the resulting corner harmlessly wide.
Clattenburg had his first big call to make just before the 10-minute mark as he opted against awarding a penalty to the hosts as Kane appealed following a tangle with Brighton captain Inigo Calderon.
With Tottenham starting to dominate, Townsend dragged a trademark long-range drive wide of Christian Walton's goal before Jan Vertonghen - the only man to retain his place from the Newcastle defeat - tested the Seagulls' goalkeeper from similar distance.
The visitors had their first chance of the night as Kazenga LuaLua latched on to a simple ball over the Tottenham back four but the former Newcastle youngster had to wait for the bounce of the ball and ended up flashing a wild volley high into the stand.
Clattenburg was again unmoved as Brighton's own call for a spot-kick fell on deaf ears after the ball struck Kyle Naughton's arm inside the box - with Dunk blazing over and Hyypia left livid with the fourth official.
Walton was on hand to make a great save to deny Soldado from close range before Lennon wasted good possession after being picked out from the corner.
That was as good as it got for Pochettino's side in the opening 45 minutes, with the Argentinian calling on compatriot Lamela at the break as Lennon made way.
The half started in a similar fashion, however, as neither Kane nor Soldado could make meaningful contact with a dangerous Naughton cross before Lamela broke finally found a way through.
The 22-year-old exchanged clever passes with Soldado before slotting home from 12 yards and relieve the tension around the stadium, with Tottenham's fans heard over the travelling Brighton contingent - a member of which was former striker Leonardo Ulloa - for the first time in the evening.
Kane came close to doubling the lead but his shot flew wide of Walton's right-hand post with Soldado, who has scored just twice this season, rattling the crossbar with a ferocious strike shortly afterwards.
The game was killed off with a little over 15 minutes to go as Kane, still without a Barclays Premier League start this season, continued to show his credentials for both club and country.
Townsend's cross was sent goalwards by a combination of Dunk and Soldado with Walton doing well to keep it out only to see Kane arrive and turn home for his seventh goal of the season.
Roy Hodgson will soon be picking his squad for the upcoming fixtures against Slovenia and Scotland and, with Daniel Sturridge injured and his Liverpool team-mate Rickie Lambert out of form, Kane will be hoping to have done enough to earn a first senior call despite his lack of league minutes.
The 21-year-old was replaced by Paulinho in the latter stages and the reception given by the home fans show that he is a player they have come to appreciate, especially with Soldado and Emmanuel Adebayor failing to hit the same heights.
Source : PA
Source: PA