There was little to split the teams in the first half, Vertonghen admits, but the Tottenham defender saluted the way his side took a firm grip of the tie in the second 45 minutes.
Son has now scored 16 goals in all competitions - he has 11 in his last 12 matches - and, whenever he has found the net this season, Spurs have won.
"3-0 is a very good result but at the same time we have to think that we have to finish the job".
"It is my job to prepare the strategy. If it was a different result, people might say I'm the worst coach in the world", he said.
"They dropped off a bit then that early goal in the second half helped". Our feeling was we never felt the confidence to play.
Dortmund's U.S. midfielder Christian Pulisic (left) and Tottenham Hotspur's Ivorian defender Serge Aurier battle for the ball during the Uefa Champions League first leg match at Wembley Stadium on Wednesday night.
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"We were able to keep them quiet in the second half and they weren't able to be clinical". That was a gift.
The Daily Express framed Pulisic and his "underwhelming performance against Tottenham" in the context of replacing star Eden Hazard (who is expected to join Real Madrid this summer) and noted that "fans on Twitter were not impressed at all by his performance at Wembley on Wednesday night".
Sancho is just 18 but his performances for Dortmund this season have been absolutely sublime, leading to questions being asked of Manchester City boss Pep Guardiola.
England winger Sancho hit top gear on several occasions in a mesmerising first-half display, leaving two Tottenham midfielders for dead and linking with Pulisic, whose shot was blocked at the last minute.
It was just the second time in Vertonghen's Tottenham stay that he had registered a goal and an assist in the same match, and team-mate Son heaped praise on the talented defender before warning that the round of 16 tie wasn't done and dusted.
Their dominance was ultimately rewarded with two further goals inside the final ten minutes, as a Serge Aurier cross and Christian Eriksen corner were finished well by Vertonghen and substitute Fernando Llorente to cap a famous European night for the north London side against the current Bundesliga leaders.