Kane's goal sends Spurs to the top of the Premier League as they continue their impressive streak of being unbeaten in the league since the opening day.
West Brom will be left disappointed after having many chances of their own. The Baggies remain inside the bottom three and are still winless this season.
Story of the match
Spurs started the brighter of the two sides, with Tanguy Ndombele powering his way through the midfield and Kane dropping deep to try and make things happen.
This positive start should have resulted in the opener around 15 minutes in. Heung Min Son was unable to get the ball out of his feet quick enough after finding himself free in the area, allowing Semi Ajayi to get across and block his effort out for a corner.
Despite struggling in the early stages, West Brom managed to settle and began to threaten. Darnell Furlong whipped a brilliant cross into Karlan Grant who was unmarked but he couldn’t get a strong enough contact on the ball to direct it goalward.
Towards the end of the half, Slaven Bilic’s side looked like the better team with their back five staying strong and nullifying the threat of the Spurs front three.
They then almost took the lead, however, Eric Dier’s flick off the line prevented Grant from tapping home Callum Robinson’s floated cross.
After the break, West Brom had their best chance of the game. Conor Gallagher whipped a superb corner into the box and Dara O’Shea rose highest to meet it but the Irishman headed just wide of the post.
Both Kane and Son could have opened the scoring soon after. Kane had a difficult header go wide and Son drilled a low effort towards goal but Sam Johnstone was able to save comfortably.
Giovanni Lo Celso, who was brought on by Jose Mourinho with 25 minutes to go, should have given Spurs the lead. The Argentinian somehow put the ball wide from six yards out after it ricocheted straight into his path.
Spurs continued to press and they finally found a goal with only two minutes left. Matt Doherty floated a cross into the area and Kane beat Johnstone to the ball to head into the back of the net.
That goal was Kane's 13th in all competitions this season and the England captain's header was enough to defeat West Brom who are still yet to win a game since being promoted to the Premier League.
Man of the Match: Harry Kane
There was only one man who could claim man of the match after the late winner.
Harry Kane was once again instrumental in Spurs' performance. The striker dropped deep all game, linking up the attack and making things happen against what was a very strong West Brom defence.
He then stepped up when it mattered to claim the three points with a great flicked header past Johnstone.
West Brom lack that clinical edge
The Baggies had plenty of chances throughout the game and will be disappointed that they have come away with nothing.
At times they were the better team and looked d more likely to break the deadlock, however, they just couldn't find the finishing touch. Grant, Robinson, and Diangana all had chances to score but never truly tested Lloris.
If Bilic's side are serious about staying up they will need to find some goals quickly as they have now only scored once in five games.
Bale still needs time
Bale struggled to get involved too much this afternoon with the back five of West Brom staying compact.
Although when he did get the ball he looked sharp and linked up well with Kane and Son in the front three.
With more game time and improved fitness, Bale is looking likely to reach top form once again in North London.