كتب : Hatem Maher
The Egypt striker, who has been in sparkling form since returning from Angola after helping the Pharaohs win the Nations Cup last month, partnered Argentinean Lucas Barrios upfront.
He helped the hosts, who led through a goal from Serbian defender Neven Subotic two minutes before the break, double their advantage in the 59th minute.
Hanover's Swiss defender Mario Eggimann diverted Zidan's free-kick into his own net to gift Dortmund a second goal.
Zidan, who has scored three league goals and dished out several assists for his teammates so far this season, was replaced with Hungarian midfielder Tamas Hajnal on 63 minutes.
Paraguayan striker Nelson Valdez added the third in the 77th minute but Hanover's Arouna Kone narrowed the gap four minutes later.
Dortmund's Kevin Grosskreutz ended any comeback hopes for Hanover when he notched home with two minutes remaining.
Jurgen Klopp's men, who atoned for their 3-1 defeat to Bayern Munich last week, remained fifth in the league table with 39 points, one behind fourth-placed Hamburg.
They need to finish at least fourth to play in next season's Europa League.