The Tottenham Hotspur striker was called up by Roy Hodgson, having scored 29 goals for his club this season, and he was brought on for captain Wayne Rooney in the 71st minute of the qualifying Group E fixture with England leading 3-0.
Within two minutes, the 21-year-old had his first goal for his country, heading home from a Raheem Sterling cross at the back post.
"I dreamed of this and it's just a bit of a blur at the moment," said Kane. "It's the best moment of my career. To represent my country at senior level is the top and hopefully I can continue to keep doing it and hopefully this goal is the first of many."
Halfway through the campaign to qualify for next year's finals in France, England are six points clear of both Slovenia and Switzerland at the top of the section.
Spain scrape past Ukraine
Reigning European champions Spain took an important step towards qualifying from Group C with a 1-0 victory at home to Ukraine in Seville.
Alvaro Morata of Juventus scored his first international goal in the 28th minute after being set up by Koke.
"In the first-half we played well and we had chances," said Spain coach Vicente del Bosque. "The second half left me with a bad taste in my mouth."
Del Bosque's side are now clear in second place in Group C, although they remain three points behind Slovakia, who won 3-0 at home to Luxembourg for a fifth win from five outings.
Germany under pressure against Georgia
Germany coach Joachim Loew is set to name a full-strength side for Sunday's clash at Georgia as the world champions look to get their Euro 2016 qualification back on track.
The Germans have picked up only seven points from their first four matches so far on the road to France 2016 and the world champions find themselves in the unusual position of joint second in Group D, three points behind leaders Poland.
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