كتب : Hatem Maher
The Egypt striker could have given his side the lead after 17 minutes but he slipped with the goal at his mercy.
He made amends on 28 minutes, converting a penalty after midfielder Yasin Oztekin was brought down inside the area.
Zidan also found the net in Dortmund's 2-0 win over Paderborn 07 earlier this week.
Kevin Grosskreutz doubled the lead over Udinese with a 35th-minute goal before Gaetano D'Agostino scored a late consolation for the Italian side.
Zidan will come face to face with his compatriot Gamal Hamza when Dortmund meet Bundesliga newly-promoted club Mainz on Tuesday.
Egyptian forward Hamza joined Mainz in the close season after his contract with Zamalek expired.