Spurs' top scorer Harry Kane cancelled out Pierre-Emerick Aubameyang's first-half strike in the 49th minute with his sixth goal of the campaign and Heung-min Son curled home the winner in the 76th.
The result put the Londoners on 13 points, three ahead of holders Real Madrid, who crushed APOEL Nicosia 6-0 away and next welcome the Germans. Tottenham, with a superior head-to-head over the Spaniards, host the Cypriots in their last group game.
Dortmund, finalists in 2013, have two points along with APOEL and have missed out on the knockout stage. They will have to sweat it out on the last matchday to see if they can finish third and claim a spot in the Europa League.
Tottenham, who had already secured a spot in the knockout stage on the previous matchday, were caught napping when Aubameyang beat the offside trap in the 19th minute but with only goalkeeper Hugo Lloris to beat he fired wide.
But Aubameyang, forced to sit out Dortmund's Bundesliga loss at VfB Stuttgart on Friday after he was suspended by his club over disciplinary issues, did put the hosts ahead in the 31st.
The Gabon international ended the goal drought he has endured since October when Andriy Yarmolenko cleverly sent him through with a flick and Aubameyang did not miss again.
Tottenham had spurned several golden chances, with Christian Eriksen and Eric Dier failing to score in the first half as Dortmund keeper Roman Buerki, criticised for a string of mistakes in recent weeks, denied them with two superb saves.
The Swiss could do nothing, however, when Kane was set up by Dele Alli and the England striker fired home from the edge of the penalty area. Alli then did even better, shaking off two markers to feed South Korean Son for the winner.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
