Turkish midfielder Nuri Sahin gave Dortmund the lead just before the break with a delicate finish.
The visitors couldn't hold onto their advantage though as Didier Konan leveled the score shortly after the restart.
The Ivorian midfielder smashed into the top corner from inside the area after being released by a throw-in.
Egypt striker Zidan was included in Dortmund's starting line-up for the second successive game to partner Paraguayan Nelson Valdez upfront.
He put in a fine display but was replaced four minutes past the hour mark, making way for Jakub Blaszczykowski.
Dortmund, whose only victory came in the opening fixture against Cologne, lie 12th in the 18-team table on just six points.
Elsewhere, Bayern Munich claimed their third consecutive win after beating promoted Nurnberg 2-1.
Ivica Olic put Bayern ahead ten minutes after the break but youngster Eric Maxim Choupo-Moting equalized for the visitors on 73 minutes.
Belgian defender Daniel van Buyten headed home with eight minutes remaining to give the Bavarians all three points.
They have 10 points from six games, just two behind joint leaders Hamburg and Bayer Leverkusen, who both played a game less.
Hannover-Dortmund highlights