A hat-trick from Pierre-Emerick Aubameyang and a goal and an assist from the teenage sensation Christian Pulisic sent the German side into the Champions League quarter-finals.
The hosts trailed 1-0 on aggregate from the first leg but Aubameyang levelled the last-16 tie after just four minutes with a header at the back post.
Dortmund cemented their grip on the tie after Christian Pulisic scored on 59 minutes.
The 18-year-old winger brilliantly chipped onrushing goalkeeper Ederson after being slid in by Lukasz Piszczek.
Aubameyang, who missed a penalty in the first leg in Lisbon, then swept in Marcel Schmelzer’s low cross two minutes later before an unmarked Marc Bartra hit the post from a corner.
The Gabon striker completed his treble with five minutes remaining as he turned in Erik Durm’s sublime pass.
Borussia Dortmund 4(4)-Benfica 0(1)