Kane took his season's tally to eight goals as he put his side ahead in the 22nd minute, connecting with Son Heung-Min's cross to flick the ball over Robert Sanchez with his head.
Spurs coach Antonio Conte chose to break the norm and play a three-man midfield, with former Brighton man Yves Bissouma deployed in the middle of the park for the visitors. But they sat back after the goal, happy to hit Brighton on the counter-attack.
Kane went down injured and was forced off just before the end of the match, but said later that it was only "a knock."
"A sore one but it's worth it when you win the game for sure. I feel good," Kane said to Sky Sports.
"It's been a difficult week to say the least [due to the passing of Tottenham fitness coach Gian Piero Ventrone] and it was nice to get the win today.
"It was a bit of a scrappy goal, Son whipped one in with pace and it went in. We managed to get the win and we know it's a difficult place to come.
"We've just got to recover and prepare for the Champions League midweek. I'm feeling good and scoring goals so hopefully that continues."
Spurs players wore t-shirts ahead of the match to honour their former fitness coach, who passed away suddenly at the age of 61 this week.
"We 100% knew we had to perform today and that was because of Gian Piero," Ryan Sessegnon said.
"It's a difficult place to come, you saw their performance at Liverpool and it was good for us to come here, keep a clean sheet and get a win. We had to dig deep."
Brighton's Lewis Dunk said he felt the match was frustrating, but credited Spurs for their performance.
"Against sides like this if you are not clinical they will get on top of you. I thought we were the better team, pinned them back. We had the better chances but unfortunately we lost," Dunk said.
Information from Reuters contributed to this report.