Argentinean striker Lucas Barrios, who joined Dortmund from Chile's Colo-Colo in the close season, opened the scoring after three minutes.
Egyptian striker Zidan doubled the advantage when he converted a penalty six minutes before the break.
He added the third on 73 minutes with a powerful shot before completing the rout one minute from time.
Zidan, who joined Dortmund from Hamburg in the summer of 2008, scored his first Bundesliga goal of the season last weekend in a 1-1 draw with Eintracht Frankfurt.
The 27-year-old was left out of Egypt's squad for Saturday's World Cup qualifier against Rwanda after failing to show up for the 3-3 friendly draw with Guinea last month.
Reports suggested that coach Hassan Shehata would not recall him for the upcoming qualifiers.