The visitors took the lead when Nemanja Vucicevic hit an early opener on 10 minutes, before Neven Subotic canceled out their slender lead one minute from the half-hour mark.
The hosts overturned the one-goal deficit when Tamas Hajnal netted Dortmund's second on 49 minutes, and Cologne's Pedro Geromel accidently slotted into his own net in the 81st minute.
Dortmund coach Juergen Klopp depended on a strike partnership of Alexander Frei and Nelson Valdez, While Zidan was a benchwarmer for the fourth match on the trot.
The Egyptian international, who has notched five goals with the Borussians this term, was introduced as a substitute only three minutes from time, and couldn't make much of an impact.
Once he came on instead of Frei he released a powerful shot, but the keeper denied it.
Dortmund now lie eighth on 43 points, while Cologne dropped to 11th place with 32 points.