Spurs went into this evening's second leg at the Westfalenstadion in control of the tie courtesy of their 3-0 triumph at Wembley last month, and they produced a textbook away European performance to complete the job in Dortmund.
It was a smash-and-grab 1-0 victory to a large extent, with their win as much down to a string of sensational saves and blocks during the first half as it was to Harry Kane's winner in the second - his record 24th European goal for the club.
That killed the tie off once and for all as Spurs ended a three-match winless streak with another famous away result in Europe, sealing their place in the quarter-finals for only the second time and the first since 2011.
Dortmund unsurprisingly attacked from the off as they attempted to undo the damage done in the second half at Wembley last month, and it took a perfectly-timed challenge from first-leg man-of-the-match Jan Vertonghen inside the penalty area to snuff out an early chance for Marco Reus.
Such heroic last-ditch defending to keep Dortmund at bay would become a feature of the first half, and captain Hugo Lloris led the rearguard action with a string of fine saves, the first of which came after 21 minutes when he reacted quickly to gather Reus's deflected strike at the second attempt.
Tottenham's defensive resolve was on show again when playmaker Christian Eriksen blocked a Mario Gotze shot deep inside his own box, although the Dane was also involved for the visitors' only clear chance of the first half.
Eriksen's through-ball sent Son Heung-min bearing down on goal, but the South Korean - who has scored more goals against Dortmund than against any other club in his career - could only fire wide after coming under pressure from Marius Wolf.
The referee checked with VAR for penalty claims against Wolf following the hint of a push in Son's back, but play soon resumed and Dortmund began to lay siege to the Spurs goal moments later.
Once again the hosts found Tottenham's defence in unbeatable form, though, with Julian Weigl the first to be denied in a quickfire flurry of chances as his initial header was well saved by Lloris before Ben Davies threw himself in front of the rebound to deflect it over the crossbar from close range.
The resulting corner was floated straight out to the edge of the box where Reus was waiting, and he connected with a stunning first-time volley perfectly only to see his goalbound effort deflect off Davinson Sanchez and narrowly over the crossbar.
Dortmund refused to relent, but Spurs somehow continued to keep them at bay and Lloris was the next to step up with a world-class one-handed stop to deny Gotze's curling shot.
The busy Spurs keeper was called upon to palm away Jadon Sancho's fierce strike moments later and made a more routine save from Paco Alcacer shortly before half time as the visitors hung on to their three-goal aggregate lead until the interval.
Dortmund enjoyed 70% possession and had 10 shots to Tottenham's solitary effort during the one-sided first half, and it looked as though it might be a similar story in the second half when Reus flashed a low ball across the six-yard box within seconds of the restart.
However, Spurs silenced the Westfalenstadion four minutes into the second period when they took the lead with their first - and only - shot on target. Moussa Sissoko was the provider as he slid a ball through for Kane, who took advantage of a splintered offside line to race through and finish confidently past Roman Burki.
The goal saw Kane move out on his own as Tottenham's leading all-time goalscorer in Europe, and more importantly it left Dortmund needing five goals to go through.
The magnitude of the task had an immediate deflating impact on the hosts, whose last remnants of hope evaporated as soon as the ball hit the back of the net, and for the remainder of the match they mostly went through the motions.
There were chances for Lucien Favre's side to at least avoid a first home defeat of the season late on as future Chelsea man Christian Pulisic looped a header onto the roof of the net and Jacob Bruun Larsen saw a deflected effort bounce kindly into the arms of Lloris.
Man of the match Lloris also made one more fine save to keep his clean sheet intact with just a minute of normal time remaining, thwarting Alcacer with his feet to cap a superb individual and team performance from the visitors.
Spurs must now wait to see who they will draw in the last eight of the competition, with Ajax the only other side so far confirmed to be joining them following their famous 4-1 win at the Bernabeu to dump out holders Real Madrid.
BORUSSIA DORTMUND (4-5-1): Burki; Wolf (Bruun Larsen 62'), Weigl, Akanji, Diallo; Sancho, Gotze, Witsel, Reus (Delaney 74'), Guerreiro (Pulisic 62'); Alcacer
TOTTENHAM (3-4-1-2): Lloris; Alderweireld, Sanchez, Vertonghen; Aurier, Sissoko, Winks (Dier 55'), Davies; Eriksen (Rose 83'); Son (Lamela 71'), Kane