The talented 20-year-old scored twice in the first half and once after the break for Jurgen Klopp's side, as the reigning champions advanced to the last eight in fine fashion
The reigning champions stormed to a 3-0 lead by half-time thanks to Mario Gotze goals either side of a fortunate Kuba Blaszczykowski strike. Mame Diouf scored a late header for Hannover before Gotze then completed his hat-trick with a driven effort and Robert Lewandowski added a fifth in injury time.
With a 12-point gap between themselves and first-placed Bayern Munich in the Bundesliga, Jurgen Klopp and his team gave a firm indication of their intention to retain their DFB Pokal title with a resounding victory over Die Roten.
The home side made a blistering start to the match and barely two minutes had passed when Gotze tapped in from close range to make it 1-0. The attacking midfielder was in the right place at the right time to smash the ball over the line after Kevin Grosskreutz had sent an inviting header across the face of the Hannover goal.
Hannover have conceded the second-highest number of goals in Bundesliga this season and their first half performance displayed clear symptoms of why that is the case, with Dortmund cutting through their defence at will in search of more goals.
Klopp's team did not have to wait long before they doubled their lead, with Blaszczykowski making it 2-0 after being set up by a stunning through-ball from Reus. There was an element of luck to the Poland international's finish, as Zieler's save from his initial shot rebounded onto the attacker and flew past the stranded goalkeeper.
Dortmund were in complete control as the game approached half-time, with each of their outfield players showing such a hunger and desire to win possession that on the few occasions that Hannover did have the ball, they did not have it for long.
Lewandowski and Blaszczykowski had further shots on goal before an off-the-ball foul from Hannover's captain Steven Cherundolo on Reus gifted Dortmund a free kick in the 38th minute. Gotze grabbed his second of the evening to make it 3-0 from the set piece, opportunistically drilling a low free kick under Hannover's jumping wall and into the bottom left corner.
After the interval the home side showed few signs of easing off despite the game seemingly won, as Blaszczykowski skewed a drive wide, Lewandowski forced a marvellous stop from Zieler and Neven Subotic headed just off target - all before the hour mark.
A fine goal from Mame Diouf made it 3-1 late on to set up a nervy finale, the former Manchester United forward heading Szabolcs Huszti's enticing cross firmly past Roman Weidenfeller and into the net.
There was still time for Dortmund to add a fourth and fifth however, Gotze completing his hat-trick with a well-struck volley, before Lewandowski completed the rout with a close-range finish after hitting the post, as Dortmund ran out easy winners in their final fixture before the winter break.