Kane has endured an injury-hit campaign, having suffered two separate ankle ligament problems.
But the 23-year-old returned to Spurs' starting line up for this afternoon's Premier League clash with Bournemouth and got straight back on the goal trail by slotting home past Artur Boruc.
The strike took Kane's tally for the campaign to 20 and he has now matched the feat Spurs legend Greaves achieved between 1966-69.
Kane told Tottenham's website: "I don't take too much notice of the records.
"But when you let me know when I've doe them it's a good feeling.
"Jimmy Greaves was Tottenham's all-time goalscorer and an unbelievable player. So to be in the same company as someone like him is incredible."
Meanwhile, Spurs swept Eddie Howe's men aside to extend their stellar home record at White Hart Lane.
The north Londoners have only dropped points in front of their own fans on two occasions this season and Kane is adamant Spurs have developed a ruthless streak.
"We got the breakthrough then killed the game off and we're very good at that.
"There were a few more chances I could've scored," he added.