Kane fired Tottenham ahead in the 48th minute when his close-range shot deflected in off Brighton defender Bruno.
It was Kane’s 26th of the season and kept him in with a chance of catching Liverpool’s Mohamed Salah, who sits ahead of the Tottenham striker on 30 goals in the race to finish as the Premier League’s top scorer.
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.
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.
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