Second-placed Real Madrid can match Tottenham's points tally on the final matchday of the group stages but Mauricio Pochettino's men will remain in first place regardless thanks to their superior head-to-head record over the holders, giving them hope of a favourable draw in the last 16.
Meanwhile, the results ended Dortmund's chances of qualifying for the knockout stages.
Pierre-Emerick Aubameyang marked his return to the Dortmund side following a club-enforced one-match suspension for disciplinary reasons by scoring the opening goal, as Peter Bosz's side sought to relieve the pressure building on the coach.
But Spurs have relished Champions League fixtures this season and they played with their usual composure and patience at Signal Iduna Park, where Dele Alli set up Harry Kane to score the equaliser after 49 minutes and Son Heung-Min completed the comeback by netting the winner with just 14 minutes left to play.
Dortmund started the game brightly and Andriy Yarmolenko combined with Mario Gotze to create a shooting chance after 12 minutes but his effort from the edge of the penalty area flew tamely into the arms of Hugo Lloris.
Yarmolenko chipped a weighted pass over the Tottenham defence for Aubameyang six minutes later, but the Gabonese striker side-footed his shot wide to the right of the net with only Lloris to beat.
Son Heung-min almost connected with a Jan Vertonghen free-kick just before the half-hour mark, but he was denied by Roman Burki and one minute later Dortmund were ahead.
Raphael Guerreiro's pass was brilliantly flicked into the box by Yarmolenko and Aubameyang raced after it before driving the ball low into the left corner of the net.
Spurs launched an onslaught on the Dortmund goal in the last five minutes of the first half but both Christian Eriksen and Eric Dier were denied at close range by superb saves from Burki, whose fingertip stop from Dier's header was particularly outstanding.
Four minutes after the restart, Danny Rose closed down a Jeremy Toljan clearance and Alli squared the loose ball to Kane on the edge of the box, giving the England striker just enough time and space to fire the ball into the net, beating Burki at his near post.
Alli tried his luck from 25 yards on 57 minutes after good work by Kane and Eriksen but the playmaker's shot drifted wide of the target.
Spurs continued to probe for a winner and Son was flagged offside as he attempted to round Burki after Alli's throughball put him in on goal
Just as the pace of the game seemed to be slowing, Alli's persistence down the left flank paid off and he forced his way into the box before knocking the ball to Son, who unleashed a right-footed shot into the top corner of the net.
Eriksen almost made it 3-1 with a header from an 80th-minute Rose cross but the ball flew wide to the right of the goal, and substitute Fernando Llorente was denied a late strike when Burki saved at his feet.
Key Opta stats:
- Tottenham have picked up 13 points after their first five Champions League group stage games, only three English sides have picked up more points at this stage since 2003/04 (current format). Chelsea in 2010-11 (15), Man Utd in 2007-08 (15) and Arsenal in 2005-06 (15).
- In contrast, Dortmund have picked up just two points after five Champions League group stage games, their worst ever points tally at this stage.
- Spurs picked up just their second away win in their last nine European outings in Germany (D2 L6).
- Tottenham are the first English side to win a Champions League away game in Germany since Manchester City won 2-1 against Borussia Monchengladbach in September 2015.
- Harry Kane has now scored 39 goals in 38 competitive appearances for Tottenham Hotspur during 2017.
- Harry Kane has scored six goals in the Champions League this season; the most goals by an English player in CL group stages (current format - since 2003-04)
- Dele Alli has assisted two goals in a single game for just the second time for Tottenham, also assisting twice against Aston Villa in March 2016.
- Son Heung-min has been directly involved in five goals in his last five starts in all competitions for Tottenham (three goals, two assists).
- Pierre-Emerick Aubameyang has scored 11 goals in nine appearances for Dortmund at home this season.