The Spurs striker scored a brace in the FA Cup victory, which lifted him above Teddy Sheringham in Tottenham's all-time goalscoring record books.
Kane is now ninth with 125 goals, bettering Sheringham's 124.
Kane is just 24-years-old and is on track to shatter Jimmy Greaves' club record of 266 if he sticks around at Tottenham.
Former Spurs defender Graham Roberts congratulated Kane on his latest achievement, sending him a message on Twitter.
Well done spurs in the next round and congrats to @HKane beating Teddy Sheringham's goal tally for spurs incredible in such a short amount of time. Coys— Graham Roberts (@GrahamRoberts4) January 7, 2018
Tottenham reached the semi-finals of the FA Cup last season and should be determined to go on and win the trophy this season.
Spurs have not won silverware since 2008, and Kane is yet to earn his first medal.
If he can go on and lift the cup with Spurs, it will help show that he does not need to depart the Lilywhites in order to do so.
But regardless of trophies, the chance to become the club's all time leading scorer might be enough to keep him around for a few years yet.