كتب : وكالات
The visitors ended the first half with a three-goal advantage before Stuttgart pulled one back after the break.
An own-goal from Khaled Boulahrouz Gave Dortmund the lead after five minutes before Lucas Barrios and Mario Gotze netted two more goals on 26 and 37 minutes respectively.
Cacau scored the consolation goal for the home side nine minutes past the hour mark.
Dortmund lost 2-0 to Bayer Leverkusen at home in their league opener last week.
Egypt ace Zidan, who had a season to remember with Dortmund before sustaining a serious cruciate ligament injury in April, is yet to get back to action.
He is expected to make a comeback in October.