Mustafi connected with an exquisite Toni Kroos free-kick to head his first international goal and give Joachim Löw's side a 19th-minute lead, but Ukraine fought back with a flurry of chances in a pulsating first half.
Manuel Neuer twice had to come to Germany's rescue to deny Yevhen Konoplyanka and then Yevhen Khacheridi, before Jérôme Boateng cleared desperately off the line from Konoplyanka.
The three-time winners fielded a relatively inexperienced team compared with the one that lifted the FIFA World Cup two years ago, yet they showed composure in the second half as they zipped the ball around in eye-catching style.
There were scares, with Neuer having to push a Yaroslav Rakitskiy free-kick around the post and Mustafi almost undoing his strike with an own goal, but the result was settled two minutes into added time when late substitute Schweinsteiger converted for 2-0. It was his first goal from open play for Germany since August 2009, and he celebrated in style.
Man of the match: Toni Kroos
Credit: UEFA.com
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