When Spurs did threaten, after Lamela played in Son, he could only drag his effort wide and they ended the half having failed to muster a shot on target.
Only heroic last-ditch defending by Alderweireld stopped Henrikh Mkhitaryan from making it two just before the break.
Aubameyang had opened the scoring eight days ago and netted his seventh Europa League goal this season after being played in by Mkhitaryan.
Son pulled one back after Neven Subotic gifted him possession just outside the Dortmund box.
TOTTENHAM (4-2-3-1): Lloris; Trippier, Alderweireld, Wimmer, Davies; Mason, Dier; Lamela, Alli, Son; Chadli.
Subs: Vorm, Rose, Kane, Onomah, Carroll, Winks, Carter-Vickers.
DORTMUND (4-3-3): Weidenfeller; Piszczek, Subotic, Papasthopoulos, Schmelzer; Ginter, Weigl, Castro; Mkhitaryan, Reus, Aubameyang.
Subs: Burki, Hummels, Sahin, Ramos, Pulisic, Kagawa,Durm.
Referee: Nicola Rizzoli (Italy).