Glenn Murray's handball from a Kieran Trippier free-kick enabled Kane to convert a first-half penalty before Erik Lamela notched late to help Spurs exorcise some of the demons of their late midweek loss to Inter in the Champions League.
Mauricio Pochettino called for his side to show fight in the aftermath of that worrying collapse and, though Anthony Knockaert reduced the deficit in the third minute of added time, he will have been heartened by the resilient response amid grim conditions at Amex Stadium.
While far from their fluid best, the visitors withstood Brighton's spell of second-half pressure for long enough to move on from the worst sequence of Pochettino's spell in charge, Kane's spot-kick setting the platform before Lamela notched what proved the winner in the 76th minute.
Toby Alderweireld, surprisingly overlooked alongside Trippier against Inter, almost broke the deadlock early in proceedings, Mat Ryan sharply saving his near-post header.
Trippier supplied the corner on that occasion and it was another of his set-pieces, this time from a free-kick, that did create the 42nd-minute opener.
Murray blocked the attempt with his arm and Kane was sent to the spot to emphatically dispatch his first goal in four appearances.
Brighton stepped up the pressure after the interval and would have equalised but for a poor Knockaert finish in a one-on-one with Paulo Gazzaniga, Spurs' third-choice shot-stopper ably deputising for injured pair Hugo Lloris and Michel Vorm.
Lamela made the reprieve count by sweeping home a Danny Rose cross and, though Knockaert went some way to atoning for his earlier miss with a tidy finish at the death, it was too late to deny Tottenham a response to the critics.
What does it mean: Pochettino can breathe easier
Pressure had been piled on Tottenham following their brittle display against Inter and even manager Pochettino was quick to call out his team's stomach for the fight.
Here, though, they answered questions over their mental fortitude, professionally navigating what loomed as a banana skin fixture.
Dembele does the job for Spurs
Mousa Dembele has filled various roles this season to differing degrees of success but, against Brighton, the midfielder looked supremely comfortable. Tidy on the ball with a commendable work ethic, he was instrumental to securing three points.
Murray makes costly mistake
Murray's action late in the first half may have been one of self-preservation, but it had significant consequences for the Seagulls.
The striker was squarely the culprit for giving away a penalty that put Chris Hughton's men behind the eight ball.
Key Opta Facts
- Brighton have only won one of their last 10 games against Tottenham in all competitions (W1 D2 L7), a home victory in April 1983.
- Tottenham have only failed to score in one of their last 17 Premier League away games (0-1 vs West Brom in May).
- Gazzaniga became the third goalkeeper to appear in the Premier League this season for Tottenham, more than any other club has used.
- Kane netted his 143th goal for Tottenham in all competitions, drawing him level with Jermain Defoe as the joint-fifth top scorer for the club.
- Lamela has scored four goals in his last four league appearances for Spurs, as many as he had in his previous 58 combined.