The Clarets took a deserved first-half lead when Chris Wood tapped home the rebound after Hugo Lloris had spilled Jay Rodriguez’s long-range shot.
At that stage, Jose Mourinho’s side seemed definitely out of sorts however the half-time introduction of Lucas Moura and Giovani lo Celso sparked the visitors.
It was Lo Celso’s exceptional through ball that compelled a rash tackle on Eric Lamela by Ben Mee and Alli scored from the penalty spot.
Burnley’s players believed they need to have had a penalty minutes later when Davinson Sanchez made a strong tackle on Wood, however nothing was given.
In a frantic finish, Lo Celso nearly scored with a curling 20-yard effort before Lloris denied Matej Vydra from point-blank range.
The result means Tottenham have now long gone 5 games without a win in all competitions – their worst run given that they went seven without a victory in the autumn of 2016.