Spurs were facing last year’s quarter-finalist in Dortmund, but Kane’s brace helped them overcome the German giants in what could prove to be a vital victory in a tough group.
More significantly for Spurs was perhaps was the fact that it got the Wembley monkey off their back after their failure to win either of their opening two Premier League games at the stadium which is their temporary home while their new ground is built.
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Defeats by Monaco and Bayer Leverkusen at Wembley last year, when they played their Champions League home games there, fuelled the belief that the national stadium, where Tottenham had won only two in 12 before Wednesday, was a jinx.
When Dortmund's Andriy Yarmolenko curled home a stunner to cancel out Son Heung-min's strike in a frenzied opening to the Group H match, Spurs feared the worst.
But Kane lashed home his first goal in the 15th minute and coolly made it 3-1 on the hour to give Tottenham breathing space.
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"It was massive to get off to a winning start," said Pochettino after the match. "It means more than three points today. To get three points against a fantastic team like Dortmund who have unbelievable players was massive for our confidence."
Tottenham were unbeaten in their final season at White Hart Lane, dropping just four points and generally dominating opponents with high-tempo football.
The question was whether they could emulate that on a bigger Wembley pitch, without their renowned 'home' atmosphere, especially against quality opposition.
This season's rather unlucky 2-1 defeat by Chelsea increased those concerns but Pochettino said the way his side dug in against Dortmund proved they could find other ways to win.
"It was tough in the first half and they dominated the game," he said. "But we were clinical. It was an important win, especially when you don't dominate the opposition but show different strengths. The performance was good but it was a day when the result was the most important thing. I hope people now stop talking about the [Wembley] curse."
Dortmund had not conceded a goal this season before Wednesday but despite their loss manager Peter Bosz, who led Ajax Amsterdam to the Europa League final last year, praised his team.
"We played very well in the first half and played some good football but we left some spaces behind the back four," he said. "It was difficult for Spurs to get the pressure on but unfortunately we didn't see that in the result."
Dortmund and Tottenham are likely to be battling for runners-up spot behind champions Real Madrid who beat Apoel Nicosia 3-0 on Wednesday to top the group.
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