Despite the 1-0 away win - their first in the league in 118 days - Tottenham remain below the relegation zone with 34 points and four games left to play. London rivals West Ham won late at home against Everton (2-1) and have 36 points.
Up to Nottingham in 16th place, Tottenham have five points.
Palhinha's winning goal came in the 82nd minute when he knocked in a 1-0 goal at the far post.
National team midfielder Lucas Bergvall was substituted after just over an hour.
It is already clear that Burnley (20 points) and Wolverhampton (17) will be relegated from the Premier League.
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