Kane converted an early penalty and struck twice more in the second half to match Alan Shearer's feat of 36 set in 1995.
The England worldwide can surpass Shearer's tally against Southampton on Boxing Day - and given the form he's in, it would take a fearless man to bet against him.
Harry Kane stole the show once more, scoring three and threatening throughout, and the Spurs boss mentioned how he sees the England forward surpassing Shearer's Premier League goal scoring record in the very near future. Going into this game, I was hoping to get a couple to take into Southampton.
Spurs took the lead when Harry Kane scored from the penalty spot after a controversial decision, with Dele Alli judged to have been fouled by Kevin Long in the seventh minute. It's a great win for us and an important three points.
Kane nearly had a second goal a few minutes later when he rolled a shot narrowly wide from an opening created by Son Heung-min, but Moussa Sissoko was guilty of squandering a glorious chance to put Spurs further ahead midway through the first half.
Following today's win, Kane said: "A few people have been speaking about it".
The Burnley fans felt so anyway, though as Alli went to ground rather easily for the penalty it was hard to know which incident they were most incensed over.
"It's a nice present for sure, it was a tough game, we knew it would be a tough game before but we know it could have been a lot more, we missed some good chances".
"You always want to finish a game off, especially away from home".