The Three Lions were on the back foot for a third of the match after defender Jarell Quansah was sent off for a high challenge.
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Kane, hoarse after celebrating with his teammates and England's supporters, said: "It was a crazy game. We had to fight and we had to find something.
"I've just been singing, I can't really talk. The occasion, the team, everything against us, we found a way."
Jude Bellingham scored twice for England in the space of 98 seconds in the first half but then conceded a penalty that the referee awarded after checking VAR images. Kane then scored a penalty on the hour-mark.
"I thought I got to the ball first, it was one of those days," Kane said. "The ref gave a lot against us. In the end it didn't matter so I'm happy."