Harry Kane’s 26th league goal of the season, following Gaetan Bong’s error, put Spurs in sight of an 11th away win.
But Brighton were behind for just two minutes, Pascal Gross levelling with an excellent penalty after Serge Aurier had caught Jose Izquierdo.
The Seagulls are without a win in six games but are eight points above the relegation zone with four games left.
Spurs almost won it through an own goal when Shane Duffy deflected Christian Eriksen’s cross a fraction wide.
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