Nobody does late Premier League drama better than the north London club, and it was no surprise to see Kane once again rescue his side with his 24th goal of the campaign.
The man of the moment was bundled over in the area by Alex Song, and Moss had no hesitation in pointing to the penalty spot.
The big issue for West Ham is that five minutes of injury time was shown on the board and the penalty was awarded four minutes and 48 seconds into stoppage time.
By the time Kane’s kick had been saved by Adrian, the clock had moved to five minutes and 54 seconds, and Moss could have ended the game before the Tottenham striker had the chance to net the rebound.
When asked if the referee should have blown straight after Kane’s miss, the West Ham manager said: “The answer to that is yes, but he wouldn’t be brave enough to do that at home, would he?
“He’ll say there was still two seconds to go. He will say when the penalty was taken, there were five seconds left, when the rebound came off, there were three second left.
“So we’re doing NFL now aren’t we? I’d like a time-keeper, to be perfectly honest with you. At the end, the referee’s not the reason why we drew. More than ourselves and a huge slice of luck for Spurs today.
“You can’t put your hands on anyone today, otherwise they will go to ground and make the referee’s mind up. You can argue whether Alex Song has made enough contact for Harry Kane to go down, but when you’re desperate like Tottenham are, you get touched and the player is going to fall over.
“Maybe we should be more like Tottenham — we stay on our feet. They’re so lucky today. There was contact on Harry Kane and he went down. Not one Tottenham player got booked today so that tells the story.”
The north London club looked dead and buried after West Ham had raced into a two-goal lead with strikes from Cheikhou Kouyate and Diafra Sakho.
But write Tottenham off at your peril. With just 10 minutes left on the clock, they showed all their fighting qualities once again, when a fortunate Danny Rose strike bounced over Adrian. And the injury-time drama from Kane could be crucial when it comes to the end of the season.
These are testing times for Pochettino, with the Capital One Cup final against Chelsea just a week away, and sandwiched in between that, a tough trip to face Fiorentina in the Europa League on Thursday.
The Tottenham head coach said: “We are always confident because we trust our players, and we never give up. This is important, we showed big character and big personality today, and good energy. Then in the last 20 minutes it was important for us, it was a big point.”
Pochettino made six changes from the team that drew 1-1 with Fiorentina on Thursday night and they started the game in promising fashion.
But after Nabil Bentaleb missed an early chance and Kane saw his shot strike the post, they were to made to pay as West Ham took a surprise lead on 22 minutes.
The ineffective Mousa Dembele lost possession which allowed Aaron Cresswell to break free down the left-hand side. The West Ham full-back played the perfect cross into Kouyate, who made no mistake heading the ball past Lloris.
Sakho made it two on 62 minutes. Mark Noble’s cross fell to the Senegal forward and from the tightest of angles he somehow managed to squeeze the ball past Lloris, even though Enner Valencia appeared to be standing in an offside position.
West Ham got away with it and were even more fortunate a minute later when Noble was lucky to stay on the pitch following a poor challenge on Bentaleb. The midfielder had already received a yellow card.
But the comeback started for Spurs on 81 minutes when Rose was in the right place on the edge of the box.
Cue late drama and there was only one man going to steal the headlines.
SPURS (4-2-3-1): Lloris 7; Walker 7, Dier 6, Vertonghen 6, Rose 7; Bentaleb 6, Mason 6 (Chadli 79, 6); Townsend 5 (Soldado 59, 6), Dembele 4 (Eriksen 45, 6), Lamela 5; Kane 8
WEST HAM (4-3-3): Adrian 7; Jenkinson 6, Tomkins 6, Reid 6, Cresswell 8; Kouyate 8, Noble 7 (Cole 67 5) (Collins 87 6), Song 6; Sakho 7, Valencia 7 (Jarvis 77 6), Downing 7
Referee: Jon Moss.