Rui Vitoria's Eagles rode their luck at the Estadio da Luz to come away with a narrow victory on home soil which gives them enormous hope heading into the return bout.
The only goal of the contest came in the 48th minute when Luisao headed a corner goal-ward which was controlled cleverly by Kostas Mitroglou who had simply pushed away his Greek colleague Sokratis Papastathopoulos to get free at the back post.
Benfica's leading scorer took another neat little touch which wrong-footed Roman Burki, allowing him to bang home from inches out.
Throughout the night, Dortmund had at least three glorious opportunities but their top scorer Pierre-Emerick Aubameyang had left his shooting boots back in Germany.
Benfica had just the one shot on target but that will not faze the Portuguese side who will feel they can gain a positive result onMarch 8 at the Westfalenstadion, while Thomas Tuchel will be working on finishing at Dortmund training over the next three weeks to avoid a similar outcome.
2016/17 UEFA Champions League - Round of 16 first leg