Red hot Harry Kane smashed a brace as Spurs saw off Dortmund.
Tottenham’s England hitman struck in the 15th minute and on the hour to end suggestions that the north Londoners cannot win at Wembley.
Son Heung Min opened the scoring after four minutes with a superb near-post strike to cap a well-worked move for the home side.
Dortmund responded in style seven minutes later when Andriy Yarmolenko curled an outstanding effort into the top corner.
There was one sour note for Spurs, however, as Jan Vertonghen was sent off late on.
The win leaves Spurs second in Group H behind Real Madrid who were comfortable winners over Apoel Nicosia.
1. The Wembley 'hoodoo' is over
At last it is over.
The insistence that Tottenham’s inability to win at Wembley had somehow been down to that supposed hoodoo. They tend to forget that the north Londoners beat CSKA Moscow here last December.
Or the fact that most of their defeats here have been against a battle-hardened Chelsea. Doesn’t fit into the narrative.
So Mauricio Pochettino’s men will be delighted to have shredded the idea that they collapse like a pack of cards whenever they run out at the national stadium.
North London now has a Champions League representative able to show strength in adversity and come out on top.
This is only the third time that Spurs have reached the Champions League group stages remember. This is a 12th appearance for Dortmund - winners in 1997 and finalists in 2013.
2. Kane is among Europe's best
He has given himself six games to shoot himself up alongside the top strikers in European football and has started off in superb fashion.
He was on the same pitch as Dortmund super-striker Pierre-Emerick Aubameyang and yet there was only one marksman we were all talking about after this.
Okay, the Dortmund keeper, Roman Burki, should probably take up another sport.
But the tenacity shown by Tottenham and England’s no.9 to wrestle free of Sokratis Papastathopoulos, race clear then shoot past Burki was trademark Kane.
His second may have taken a slight deflection but, in truth, once Eriksen teed him up in the box on the hour there was only going to be one outcome.
3. Sanchez will be come big asset for Spurs
He established himself as one of the top young defensive talents in world football last season. Peter Bosz, his coach at Ajax, is now the boss of Dortmund and described Sanchez this week as ‘a monster’.
"What surprised me was that he played the final of the Copa Libertadores last year, which he won," said Bosz.
"And without any vacation he came to us (Ajax) and after one week he played. He played the whole season. He was never injured.
"Without the ball, he is a monster. He is strong in the air, he's fast. With the ball, in Ajax, we had a certain way of playing which he had to adapt to.”
If Sanchez looked uncertain against Dortmund it was because he was up against a side who move the ball superbly while he is still finding his feet.
Make no mistake, however, he will become an asset for Spurs. A big one.
4. Aurier could be a bargain at £23m
Pochettino was never going to play Kieran Trippier in this one ahead of Aurier, a seasoned Champions League campaigner.
What a bargain the £23million Frenchman is at less than half the price of Kyle Walker - and three years younger.
Aurier’s pace and power were vital during the first half as Spurs had to dig in to cope with Dortmund’s response to Son’s opener.
Daniel Levy has pulled off some great, late, summer deals but this one is a corker.
5. Pochettino got it right
Credit to the Spurs boss who said his team would be ready. Who insisted his side had learned from their failure to get out of the group in this competition last autumn.
He has always made it clear that the issue was not the stadium.
The football did the talking here as his men took another significant step in their development against an accomplished Dortmund team. Pochettino prowled the touchline at 3-1, determined not to allow his players to rest on their laurels.
The loudest voices inside the national at that point were the home fans, belting out a rendition of ‘When The Spurs Go Marching In’.