The match was moved to Leipzig's stadium after the pitch at Dessau's Paul Greifzu stadium was left unplayable after being sprayed with chemicals by unknown culprits.
Werner, who struggled in his final season with Chelsea, looked back to his best as he made clever runs and found space in the box to score three times while he also assisted Andre Silva to give Leipzig a 4-0 half-time lead.
Leipzig dominated possession while Ottensen failed to register a single shot on target in the game.
The second half was also one-way traffic as Silva scored his second while Emil Forsberg and Christopher Nkunku got on the scoresheet. Dani Olmo completed the rout with a goal in the 90th minute as Leipzig advanced to the next round.