The 21-year-old has reached that total in all competitions, including 20 in the Premier League, and is the first Spurs player since Gary Lineker in 1991-92 to reach 30 in a season.
Kane, who has been nominated for the PFA Player of the Year and PFA Young Player of the Year awards, has become a fans' favourite at White Hart Lane this term, lauded as "one of our own" after coming through the youth ranks since the age of 11.
"I'm very proud but there are five games left and, hopefully, I'll get a few more goals," Kane told Sky Sports.
"We deserved it today. We played well. We've had some disappointing performances in the last couple of weeks and we wanted to put that right.
"I had a couple of chances and the keeper made some good saves but I'm delighted to get back on the scoresheet."
Kane also scored 80 seconds into his England debut as a substitute in a 4-0 win over Lithuania at Wembley last month.
The youngster showed his killer instinct in front goal at St James' Park, scoring the third against Newcastle, and manager Mauricio Pochettino was delighted he equalled Lineker's tally.
"It's fantastic, congratulations to him because he deserves this moment, it's historic, the first time since Gary Lineker in 1992," Pochettino told Sky Sports.
"I think he needs to pay for a dinner this week for his team mates. The team work a lot and try and help the striker score."
Sixth-placed Spurs are level on 57 points with Liverpool in fifth having played a game more and Pochettino is pleased they are still competing for a European place with five games left.
"Our performance was good. We deserved the win as we were better than Newcastle," he said. "It is important because we are in a position where we can fight for something until the end of the season.
"It's very important to finish the season on a good level and then we have to analyse."
(Reporting by Michael Hann; editing by Ken Ferris)
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