Burnley may even feel aggrieved as Chris Wood was penalised for handball as he was bearing down on goal - as Eric Dier's attempted clearance struck the New Zealand international's arm from close range.
Story of the match
The first half was far from explosive, as the Clarets remained stubborn and kept their structure, frustrating the Spurs attack.
The most major moment in the first 45 minutes saw Toby Alderweireld struck by an accidental flailing arm from Ashley Barnes, leaving the Belgian defender needing his head heavily bandaged.
The home side did have the ball in the back of the net during the first period, but Barnes was rightly flagged offside after he put the ball beyond Hugo Lloris.
Ashley Westwood did force a save out of the Frenchman towards the end of the first half, striking low and hard from the edge of the box but not accurate enough to put his side in front.
Burnley continued to be the better side from the start of the second half, and Chris Wood had the first good chance when his deflected effort dropped just over the bar.
Controversy also ensued when Wood found himself bearing down on goal after Eric Dier's clearance struck him on the arm at point blank range.
Harry Kane then turned defensive wall from emphatic forward by making a last-ditch goal-line clearance from James Tarkowski's attempt.
Burnley's efforts had Tottenham startled, and left Jose Mourinho on the touchline yelling instructions for his side to get forward and play more risky passes in the final third - to which Tanguy Ndombele responded.
Tottenham's record signing controlled the ball neatly before turning and playing a sublime ball to Heung-Min Son, who was tracked brilliantly by Kevin Long who made a fantastic block on the Korean's shot.
The pressure mounted on the Clarets, as Spurs looked for a winner, which they got when substitute Erik Lamela's pin-point corner was flicked on by Kane into the path of Son who powered his header home.
The goal made it the 29th time the duo have combined for a Premier League goal, placing them just behind Frank Lampard and Didier Drogba in the all time goal combinations table for the Premier League.
Spurs could have doubled their league through Lamela, but the Argentinean's miscued volley meant the score remained level at full time, leaving Burnley in 18th with just one point and Tottenham in 5th with 11 points.
Man of the Match - Harry Kane
Is there a player that has made a better start to the season than Harry Kane? Even when he's not scoring, it's easy to still run out of superlatives for the England captain.
A goal-saving clearance and another fantastic assist gives Kane man of the match, in a game where very few shone.
That makes it eight assists for Kane and eight goals for Son so far this season in the league - a dynamic duo out to break records and help Spurs to their first trophy in 12 years.