Kane's solitary strike earned a 1-0 win over champions Manchester City, taking him onto 267 goals for Tottenham, one clear of Greaves.
The win put a dent on Manchester City's title aspirations as they failed to close the gap on leaders Arsenal while Spurs moved to within one point of fourth place Newcastle United in the race for the top four.
Kane's winning goal also saw him reach 200 Premier League goals, joining Alan Shearer and Wayne Rooney as the only players to reach that figure.
Kane told Sky Sports after the game: "It's a magical moment. I was so desperate to do it with a win – once we went 1-0 up, it was about the clean sheet.
"To do it in front of the fans is a special moment. There has been so much talk about it, I just wanted to get it done. So, to do it in a big game against one of the best teams in the world is special.
"[Greaves] is a complete hero, one of the best strikers to play the game, so to be in that conversation is special. And to overtake him is a huge moment for me."
"When I started playing regularly, it wasn't even in my imagination to score 200 Premier League goals," he added.
"To be there now is exciting, and I've got plenty of years left, so there will be a few more to come."
