Adam Webster headed Brighton into a deserved 37th-minute lead, the centre-back’s third Premier League goal of the season.
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However, Spurs were level eight minutes after half-time when, at the second attempt, Harry Kane lashed home his fifth goal in eight Boxing Day games.
Then, with just 18 minutes left, Alli’s deft touch gave Tottenham all three points, lifting them up to seventh in the Premier League ahead of the afternoon matches, while Brighton stay 13th.
Nigeria defender Leon Balogun was not listed for the game by Brighton.
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