Youngster Marvin Ducksch tapped home the opener for Dortmund before Lewandowski made it 2-0 with a header.
The Polish striker had been expected to leave Dortmund in the summer but has now scored in two successive pre-season games.
Dario Lezcano got one back for the Swiss side but then Mkhitaryan swept home his second goal in pre-season just before half-time. The Armenian international chose Dortmund over Liverpool when leaving Shakhtar Donetsk for £23.7m in the summer.
A second-half goal from Marco Reus completed the victory.
A strong Galatasaray side needed a last minute winner from substitute Wesley Sneijder to secure a 2-1 win at Meadow Lane against English League One outfit Notts County.
A Dany Nounkeu own goal had given County an unlikely lead and it was not until the 80th minute that Burak Yilmaz equalised for the Turkish giants. Sneijder and Didier Drogba both played the entire second-half of the match.
Bundesliga side Hamburg enjoyed a 3-1 success over Belgian champions Anderlecht in Austria. An own goal, Ivo Ilicevic and Valmir Nafiu were their scorers.
Hertha Berlin, who will return to the Bundesliga league next season, also enjoyed a victory - 2-0 over Polish outfit Wisla Krakow.
New Benfica signing Lazar Markovic scored twice as the Europa League finalists beat Sion 3-2. The 19-year-old Serbian international signed a five-year-contract with Benfica after joining from Partizan Belgrade in the summer.
Ligue 1 side St Etienne prepared for their Europa League qualifying campaign with a 3-1 win over Ligue 2 side FC Istres in Valenca. Romain Hamouma, Renaud Cohade and Idriss Saadi got the goals.
- Sports & Recreation
- Wesley Sneijder