The 28-year-old, playing in his 139th match away from home in England's top flight, took sole possession of the mark he shared with Wayne Rooney coming into the match. It took Rooney a further 104 games to hit 94 on the road.
Kane doubled the visitor's lead with his record strike just before the hour mark, running on to a pinpoint through ball from Rodrigo Betancur and smashing a left-footed strike past Sanchez to make it 2-0.
"We got ahead in the game and then I think we controlled it. Overall it was a really good night away from home," Kane said.
"Sometimes you need a bit of luck to go your way to break the deadlock and that's what happened and from there we controlled it. We played good football we just have to keep winning games."
The result moves Antonio Conte's side up to seventh in the table with 48 points from 28 matches, while Brighton remain in 13th having secured 33 points in their 29 games.
"We're very happy because Harry is scoring a lot. He started this season and struggled a bit, because he didn't score a lot," Conte said. "Now we're very happy because as a manager I know I have a world class striker that in every game he can score."
Kane was heavily linked by the British media with a switch to champions Manchester City last summer, but the 28-year-old England international remained in North London.
"To have Harry in your team makes you stronger," Conte said. "Harry is starting to understand with this team, with the way we're playing, he has every game many chances to improve his record and score and enjoy.
"I'm seeing that he's enjoying playing with us together and with his team mates and with this way we're playing."
Brighton failed to really trouble Tottenham keeper Hugo Lloris as they slumped to a sixth successive league defeat although they are well clear of relegation trouble.
There was certainly a large slice of luck about Tottenham's opening goal. A rather languid move ended up with Kulusevski having a shot at goal and the ball glanced the leg of Romero to wrong-foot Sanchez.
Tottenham's second was clinical.
Brighton were actually enjoying their best spell of the game, but when a move broke down Bentancur's incisive pass released Kane who had timed his run to perfection.
The England captain drilled a shot low inside Sanchez's near post before the keeper had time to set himself.
Tottenham could have extended their lead late on with Kane having a penalty appeal turned down and setting up Sergio Reguilon whose shot was saved.