The front man added to his early penalty with two well-taken second-half strikes in a game we dominated in terms of clear chances and, in truth, should have won by more.
It was the Academy product's SEVENTH treble of 2017 and one which saw him equal Alan Shearer's record for Premier League goals scored in a calendar year with a total of 36.
It was also our first away league win in six attempts as we climbed above the hosts and Arsenal into fifth.
Moussa Sissoko was earlier denied one-on-one by home goalkeeper Nick Pope as we weaved a path through the Clarets' midfield with relative ease in the first half before Heung-Min Son blazed over with the goal gaping after the break.
Davinson Sanchez, who made his Spurs debut in the reverse fixture in August, was superb at the back on his return from suspension - one of a number of positives from a good overall display in our last match before Christmas. Next up, Southampton on Boxing Day!
There were four changes to the team that to at Manchester City a week ago, with Serge Aurier and Ben Davies coming in for ex-Burnley man Kieran Trippier and Danny Rose at full-back. Sanchez returned to take his place in the centre of defence, with Eric Dier moving into central midfield at the expense of Harry Winks, who missed out with a minor ankle problem. Sissoko also started in place of Mousa Dembele. Burnley, sixth going into the weekend, were without influential defender James Tarkowski.
GOAL: BURNLEY 0-1 SPURS - HARRY KANE (PENALTY) - 7mins
We made a positive start and took the lead after seven minutes from the penalty spot. Good work by Christian Eriksen saw Dele Alli pick up possession on the right side of the area and he was impeded by Kevin Long as he came across to challenge him, with referee Michael Oliver immediately pointing to the spot. Kane made no mistake, sending Pope the wrong way.
SAVE: POPE DENIES SISSOKO ON THE BREAK WITH DOUBLE SAVE - 22mins
Kane nearly had a second when he rounded Pope but drilled into the side netting from a tight angle after reacting quickest to Dele's deflected shot, but we had a big chance to double our lead midway through the first half. Eriksen started a quick break following Burnley's corner and Dele spotted Sissoko steaming through the middle but Pope saved with his legs when one-on-one with the France international, before denying him again on the follow-up.
Above: Davinson Sanchez and Scott Arfield.
CHANCE: SON SQUANDERS GREAT OPPORTUNITY - 56mins
Burnley had started to match up to us from the midway point of the first half but we still had that extra bit of quality to create chances. Sadly, we were unusually wasteful with them and when Aurier burst through on 56 minutes and squared for Heung-Min Son, it looked for all the world that the in-form forward would score, only to balloon over the top with just the keeper to beat. Kane almost sprung Eriksen in moments later but over-hit his pass to the Dane before seeing his own deflected shot zip just wide of the far post.
GOAL: BURNLEY 0-2 SPURS - HARRY KANE - 69mins
Kane showed good composure to slot beyond Pope and make it 2-0 with 21 minutes left to play. The Burnley defence was open wide as Sissoko prodded through to him, allowing the striker to finish from a central position.
GOAL: BURNLEY 0-3 SPURS - HARRY KANE - 78mins
Kane's ever-burning desire to win the ball led to him completing his hat-trick. He made a challenge near the left corner of the penalty box to get the ball, Davies picked it up and found Dele, who threaded it through the defence and back to Kane to drill across Pope with his left foot. Sam Vokes headed in at the other end moments later but was adjudged to have fouled Hugo Lloris as he climbed above him, with the keeper then forced to scramble Ashley Barnes' header away down by the post, but the game was over as a contest by that point.
MAURICIO POCHETTINO SAID
"It was a fantastic performance. I'm so pleased and congratulate the players. I'm so happy because the three points were so important for us. We dominated, created chances and from the beginning, the team was hungry to go and fight and battle for the victory and that's what pleased me most."
ERIC DIER SAID
"We played really well. It's been a difficult week for us after last Saturday (at Manchester City) and we had to bounce back in the right way and we did that. There was a determination. We knew how big and important this game was for so many different reasons and we were determined to come out and show the right attitude from the start and take control, be aggressive with and without the ball and we did that."
Burnley (4-5-1): Pope, Bardsley, Long, Mee (c), Taylor, Arfield (Wells 86), Cork, Hendrick (Vokes 71), Defour, Gudmundsson, Wood (Barnes 35). Subs: Lindegaard, Lowton, Westwood, Walters.
Spurs (4-2-3-1): Lloris (c), Aurier, Sanchez, Vertonghen, Davies, Dier (Lamela 83), Sissoko, Eriksen, Dele (Llorente 86), Son (Dembele 77), Kane. Substitutes (not used): Vorm, Trippier, Foyth, Rose.
Goals: Spurs - Kane 7 (pen), 69, 78.
Yellow cards: Burnley - Defour 88; Spurs - Dele 4, Sissoko 57.
Referee: Michael Oliver.
MAN OF THE MATCH
The match ball wasn't the only thing Harry Kane took home after the game at Turf Moor. With 91 per cent of fans' votes on social media, he was also named Man of the Match!
It's the return of a once regular Boxing Day fixture on Tuesday as we welcome Southampton to Wembley for a 12.30pm kick-off. Throughout history, we've often found ourselves pitted against the Saints on December 26, but this will be our first Boxing Day meeting with them since 2001, when James Beattie gave the hosts a 1-0 win. The Saints drew 1-1 at home with Huddersfield Town on Saturday afternoon, dropping to 13th in the table as a result.