But Mauricio Pochettino’s side, who face Manchester United at Wembley on Saturday, left the Amex Stadium frustrated after conceding an equaliser two minutes after Kane’s opener.
Albion drew level when Pascal Gross slotted home a penalty awarded for Serge Aurier’s foul on Jose Izquierdo.
Tottenham have gone two games without a league victory, but they are still in pole position to qualify for next season’s Champions League via a top four finish.
They are in fourth place, eight points ahead of fifth placed Chelsea, who have only five matches left to close the gap.
“It was a difficult game, the first half was even and the second half we started really well. We scored but in the next section we conceded,” Pochettino said.
“We created chances but not enough to win the game. The draw is a little bit disappointing because the intention was to get all three.”
Brighton are eight points clear of the bottom three and should be safe from relegation at the end of their first season back in the top-flight.
With the FA Cup representing Tottenham’s last chance of silverware this season, Pochettino — yet to win a trophy in his four years with the north London club — made six changes from the team beaten 3-1 by Manchester City on Saturday.
Belgium defender Toby Alderweireld was handed his first league start since October in place of Davinson Sanchez, while Dele Alli, Kieran Trippier, Mousa Dembele and Eric Dier were rested.
Pochettino defended his selection, saying: “We were thinking of giving the team fresh legs because Saturday’s game against Manchester City was tough mentally and physically.
“We have a squad good enough to win games. This result was not because we rotated the team.
“Everyone is ready to play but Brighton was a very difficult opponent and we need to give credit to them.”
Lucas Moura, given his first league start as part of Pochettino’s switches, threatened with a powerful drive from distance as Tottenham tried to take control.
Tottenham winger Son Heung-Min went closest to breaking the first-half deadlock with a low shot which forced a fine save from Albion goalkeeper Mat Ryan.
Pochettino’s men took the lead when a poor pass from Gross, followed by indecision from Gaetan Bong, allowed Son to slip into the area.
The South Korean did well to keep control and the ball eventually broke for Kane to sweep home.
However, Brighton were back on level terms in the 50th minute as Izquierdo won a penalty by inducing Aurier’s rash challenge.
Regular Brighton penalty taker Glenn Murray, who has missed twice from the spot this season, stepped aside to allow German midfielder Gross to shoot under Hugo Lloris’s dive.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)