The visitors had executed their game-plan to perfection, and seemed certain to enter the interval level, until Kevin Friend awarded Antonio Conte’s men a penalty deep into stoppage time.
The referee walked over to check the monitor when liaising with VAR Stuart Attwell after striker Ashley Barnes was adjudged to have handled Davinson Sanchez’s flick on.
England international Harry Kane stepped up in the 48th and tucked the ball into the corner, with Nick Pope rooted to the spot.
Barnes almost atoned for his error in the second half, but his thumping attempt from outside the penalty cannoned back off the post with Hugo Lloris well-beaten.
It ended 1-0 at the Tottenham Hotspur Stadium. Here are the player ratings.
England international Harry Kane stepped up in the 48th and tucked the ball into the corner, with Nick Pope rooted to the spot.
5. Matt Lowton 7
Played on the left hand side of a central defensive three and stood up to the challenge. Picked up intelligent positions inside the box to clear threatening deliveries and calm in possession when Burnley played the ball across the back. Solid afternoon for the full back. Photo: Alex Livesey
6. Nathan Collins 9
Another remarkable display from the 21-year-old. The Republic of Ireland international's potential is frightening. Showed no fear when faced with Kane, Son and Moura and his confidence rubbed off on his team-mates. Solid as a rock in defence, his composure on the ball defies his years and he carried the ball out from the back well. Made a stunning clearance off the line to deny Kane and threaded a wonderfully incisive pass into Cornet for the Clarets' best chance of the first half. Photo: GLYN KIRK
7. Dwight McNeil 7.5
Played with freedom in a midfield three, moving effortlessly across the pitch to effect play on both sides. Worked hard against the ball and popped up in predominantly central positions after the break, switching play to both Roberts and, particularly, Taylor. Excellent in possession. Photo: Ryan Pierse
8. Maxwel Cornet 5
The Ivorian international found it hard to get involved most of the time and lacked the physicality to really challenge the Spurs defence. Had the best chance of the game for Burnley, which would have put the visitors ahead, but was foiled by Lloris when through on goal. Photo: LINDSEY PARNABY