Mahmoud Dahoud's injury gave a start to Emre Can, as on-form striker Erling Braut Haaland sat out in favour of Jadon Sancho, who came on as a substitute in the previous three league encounters.
Can got stuck into action earlier on after a ball from the right whistled narrowly around the far post with winger-cum-fullback Mohamed Drager looking on nervously.
Dortmund continued threatening after Thorgan Hazard latched onto a long pass down the middle before bringing Leopold Zingerle 17 minutes in.
Both sides finished the half with chances, as Christopher Antwi-Adjei switched to the left to fire over from close range while Julian Brandt steered Achraf Hakimi's ball wide of the mark at the other end.
Dortmund were ahead just under ten minutes from halftime after Zingerle pushed Can's cross from the near post straight to Hazard, who slammed home comfortably.
It was two after 57 minutes when a cross into the six-yard area from Brandt found Sancho, who ran through the middle to beat Zingerle with a simple tap-in.
The home side found a lifeline after 71 minutes as Uwe Hunemeier fired in from the penalty spot after Can was flagged for handling a shot in the area.
Lucien Favre's boys regained their two-goal advantage after Sancho found possession near the area to complete his brace three minutes later.
Hakimi gave his side a fourth goal in the final three minutes after firing home from a tight angle on the right side of the area.
It got worse for Paderborn in the final minute, with Mario Schmelzer running onto a ball through the middle to beat Zingerle before Sancho had the final say when he completed his hat-trick at the death after being afforded space to fire home following a counter-attack.