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Spurs came into the game at Wembley on the back of three successive Premier League wins, while Dortmund had drawn their last three matches.
However, it was the visitors who enjoyed the upper hand in the first half with Spurs struggling to get out of their own half for the majority of the time.
But Spurs turned the game on its head after the interval and completely dominated with Heung-Min Son, Jan Vertonghen and Fernando Llorente all on the scoresheet to give the north Londoners a healthy lead to take to Germany for the second leg.
Serge Aurier, Juan Foyth, Toby Alderweireld and Lucas Moura were all handed starts as Tottenham made four changes from the side that beat Leicester 3-1 on Sunday.
Dortmund also boasted four changes to the side which drew against Hoffenheim as Christian Pulisic, Thomas Delaney, Omer Toprak and Dan-Axel Zagadou all started.
Moura went close to breaking the deadlock in the eighth minute when he latched on to Davinson Sanchez’s knockdown and fired an effort inches wide.
Dortmund’s first real attempt came on 14 minutes when Pulisic pounced on an error by Foyth and hit a low left-foot strike towards the near post, but Hugo Lloris made the save with his legs.
However, the Germans upped the tempo and enjoyed a good spell of possession with Delaney getting a strike on target on 36 minutes which Lloris could only parry but Sanchez was on hand to clear the danger after initially making a mess of it.
Lloris was called upon again just before half-time when he pulled off a superb save to claw away Zagadou’s header following more good work from the ever-lively England international Jadon Sancho.
After struggling for the majority of the first half, Spurs had a dream start after the break when they went ahead on 47 minutes.
Vertonghen curled a lovely cross into the area and Son was on hand to volley in his 16th goal of the season.
The goal clearly lifted Spurs and they went in search of a second with Vertonghen going on a surging run and firing over the top, before Christian Eriksen hit a low strike which Roman Burki got down to gather on the hour.
A minute later Alderweireld got up to meet Eriksen’s corner from the left at the front post but his flick header was straight at Burki.
Dortmund almost created a chance out of nothing when Pulisic tricked his way into the area, but Sanchez produced a vital interception just as he was about to pull the trigger.
On 69 minutes Mahmoud Dahod lined one up from outside the area but his shot was straight down the throat of Lloris who easily gathered.
Spurs responded again and Moura was unfortunate as a corner from the right dropped into his path on the left side of the area but his goalbound effort was blocked by Delaney and looped over the top.
The hosts continued to dominate and they were rewarded with a second goal on 83 minutes when Vertonghen raced into the area to meet Aurier’s cross from the right channel and cushioned his volley past Burki from close range.
It was 3-0 on 86 minutes when Eriksen’s corner from the left was met by substitute Llorente who guided his downward header into the corner of the net.
Raphael Guerreiro went close to grabbing an away goal for Dortmund in the 90th minute but his curling strike from outside of the area drifted just wide of Lloris’ upright.