But now another's name is on their lips: 20-year-old midfielder Harry Winks who marked his first Premier League start with Tottenham's first goal.
The newcomer pounced to cancel out Michail Antonio's first-half opener for West Ham and ran ecstatically to the stand where his family were celebrating a dream come true for a Spurs-supporting youngster who joined the club when he was at primary school.
He gave them a wave before being enveloped in a bear hug by Mauricio Pochettino, his manager and then a wave of happy team-mates.
The Argentinian was equally touchly feely after Kane's late double had prevented Manuel Lanzini's penalty, controversially awarded for off-the-ball holding from a corner by Vincent Jansson, from giving West Ham manager Slaven Bilic respite from a dismal start to the season.
Pochettino hugged all his players on the final whistle and revealed the feel good factor carried on into the dressing room as Tottenham carried on their unbeaten league start to a twelfth game and ended a seven-fixture winless run in all competitions.
"After seven games, for the players that victory was very important," he said. "And it was emotional - how we celebrated the goal with Harry and how we celebrated at the end.
"I wait for all the players at the end to give a big hug. Every one. It’s true I put a lot of pressure on my players in the changing room - I like my hugs!"
Winks, who had been elevated to the England Under-21 squad this month as well, won't forget this weekend in a hurry.
"That is one moment in my life I can never repeat," he said. "Being a Spurs fan as well, scoring the equaliser against West Ham, it was brilliant.
"I could have kept running. I had a burst of energy and saw my family and pointed to them. It was unbelievable.”
And then he hugged his boss. He added: “He’s given me my chance and put me into the first team. That was a ‘thank-you’ to him for everything he’s done for me.”
Bilic's decision to take off play-maker Dmitri Payet for defender Havard Nordtveit with West Ham 2-1 up with five minutes remaining backfired spectacularly
Kane levelled after goalkeeper Darren Randolph, in for Adrian, could only shovel a cross from substitute Son Heung-Min to where he was lurking at the back post. Then the England striker won it from the penalty spot after Son had been tripped by Nordtveit's ill-judged slide in.
Bilic, who saw defender Winston Reid sent off for clashing with Kane moments before the final whistle, said: "It was five minutes to go, we were 2-1 up, from my point of view, from our point of view, it was a logical move to put on a fresh body. He was excellent today but we thought 'OK it's the end of the game, we are winning, let's hold on'.
"Sometimes an opponent like Spurs they are forcing you to sit back which they are very good at of course. The extra quality they put from the bench they raise the game so that was why we didn't do it before. We wanted to score a third one but when we see them coming then you think you can resist it with one more player, a fresh body for five or seven or eight minutes."Reuse content