The three goals the Tottenham Hotspur striker scored took his total for the year to 39, ahead of the mark of 36 set by Alan Shearer for Blackburn Rovers in 1995.
And Shearer sent his congratulations to Kane via Twitter.
Kane was delighted to beat the record of the Premier League's leading scorer.
"To be compared with Alan Shearer is great," Kane, who is top scorer with 18 goals in 2017/18, said. "It’s a great feeling to be up there with his record."