Kane should have grabbed his record goal much earlier in the game. Around the fifth minute, the striker stole the ball from Brighton goalkeeper Robert Sanchez before shooting wide, despite finding space to round the keeper and face an empty net.
New signing Dejan Kulusevski made several positive contributions and played a key role in the opening goal when his powerful deflected shot was deflected by Cristian Romero.
Minutes before half-time, the former Juventus winger was back on after latching onto a through ball and rushing into the box. However, his shot was saved by Sanchez in the Brighton goal.
The second half continued like the first, with Tottenham looking to deliver the final blow to their opponents.
Just before the hour mark, their iconic striker was on hand to do what he does best. Rodrigo Bentancur capped a practice in the middle of the park with a perfect pass for Kane, who controlled the ball before calmly flicking it past Sanchez with his left foot.
Obviously still in the mood to score goals, the striker caught a bottle thrown at him with a good volley during his celebration.
His second-half goal means he has scored 95 goals in 139 away appearances in the Premier League, becoming the competition’s all-time leading goalscorer in away games despite having 104 less appearances than Wayne Rooney, second.
The goal also gave Kane another milestone as the striker overtook Frank Lampard to move into fifth overall with 178 Premier League goals.
The score remained at 2-0 and Antonio Conte would be happy as his team picked up some crucial away points.
Kane will be hoping to add to his seven goals this season when Tottenham host Westham on Sunday.