Christian Eriksen's stoppage-time strike broke Burnley's brave resistance as Tottenham maintained their pursuit of the top two in the Premier League.
It looked as if the Clarets had held on to a deserved point, but in the 91st minute substitute Eriksen popped up in the area to slam his shot high past Joe Hart.
The Burnley goalkeeper had earlier pulled off a magnificent save to deny Erik Lamela on a day when the home side produced very few clear-cut chances.
The victory moves third-placed Spurs to 39 points and within three of Liverpool in second. Burnley remain in 17th with 12 points - two points above the relegation zone.