Jacob Bruun Larsen had the Clarets ahead before Pedro Porro and then Micky van de Ven struck for Tottenham.
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Afterwards, Spurs boss Ange Postecoglou said: "We were dominant enough, their keeper was outstanding today and we had enough chances.
"It's always difficult when you lose four matches in a row and it is only natural there will be a bit of anxiety and a bit of stress there.
"For the most part I think we handled the game well and we finished the game strong.
"It should have been a more comfortable victory but the most important thing is we won the game."
