After substitute Alex Oxlade-Chamberlain had given the Three Lions the lead at Hampden Park, Scotland appeared to be on the brink of securing what would have been a memorable victory following two superbly-struck free-kicks from Leigh Griffiths.
But Kane stunned the crowd two minutes into injury time when he volleyed home a flawless pass from Raheem Sterling, a goal that prevented what would have been England's first World Cup qualifying loss since a defeat to Ukraine in 2009.
"I have said before I would love to be England captain", said Kane, who had previously been denied the chance to represent Southgate's team by injury and whose goal was his first for the national team in 13 months. "So to score that goal was a special feeling for me", said the striker. "I did not know whether the keeper was going to come, so when I saw him stay on his line ... what a ball it was, and it was just a good side-foot into the net".
And Southgate was disappointed England only emerged with a point in a game he felt they controlled.
"[It was] a game we should win, a game we were in total control of", said Southgate.
"We don't beat England very much", said the Scotland great. You need to give people game time; in the past one or two goalkeepers have given up global football because they haven't had the chance.
"They get two goals from nowhere, but we still managed to claim a point".
"The challenge is how do we become the best team in the world?"
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Scotland next travel to Lithuania and then host Malta and Slovakia, who are four points ahead of Strachan's side in second, before facing Slovenia away from home in their final group game.
England manager Gareth Southgate said his team's last-gasp 2-2 draw against Scotland demonstrated the kind of mental fortitude he is trying to instil in his players.
England trained with the Royal Marines in the build up to the match, and Kane praised the determination of the squad. There was a great atmosphere and the way the game panned out, it was a good point.
"On our day we can match any-body".
"I don't think it was tougher than what we expected because we always expect to have tough games, especially against your rivals".
"We are in pole position and it's in our hands". I will look at the players and tell them you have to keep coming back and taking knocks like that. He told me just before training on Friday.
"We got ourselves into decent positions, but could not finish".
The draw means England's cushion at the top of Group F has been narrowed to two points, but there remains confidence within the group that it is a matter of when rather than if they qualify for the World Cup.
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