Valencia defender Mustafi powered home the opener from Toni Kroos’s free-kick after just 19 minutes of Sunday’s game.
And Schweinsteiger wrapped up the win in injury time, moments after coming off the bench.
However, Germany were also thankful to captain for the night Neuer as he made stops from Yevhen Konoplyanka and Yevhen Khacheridi, while Jerome Boateng made a spectacular clearance off his own line.
The giant Bayern Munich goalkeeper flew to his right to turn Sevilla winger Konoplyanka’s curling effort behind after a slip from Mustafi after just five minutes.
However, the absence of the injured Mats Hummels and Antonio Ruediger played into German hands for the opening goal as Mustafi made the most of his chance to start in their absence with a bullet header from Kroos’s free-kick.
Neuer came to Germany’s rescue again with brilliant reflex save to tip over Khacheridi’s header, but Loew’s men could just as easily have been 2-0 up moments later when Sami Khedira shot too close to Andriy Pyatov.
Ukraine ended the half on the front foot as only a remarkable acrobatic clearance from Boateng prevented the dangerous Konoplyanka from levelling, with English referee Martin Atkinson helped to make the right call by goal-line technology.
Even when Ukraine did finally beat Neuer they were denied by the offside flag when Andriy Yarmolenko tapped home seven minutes before the break.
Germany enjoyed more control after the interval with Ukraine’s twin threats of Konoplyanka and Yarmolenko kept in check.
However, they were restricted to efforts from long range as Khedira was again denied by Pyatov with a fierce drive from 25 yards.
Pyatov got down well to save from Mario Goetze and Thomas Mueller as spaces began to open up with Ukraine pushing more bodies forward in search of an equaliser.
They finally put the result beyond doubt in injury time when Mesut Ozil’s inch-perfect cross from the left was fired home by substitute Schweinsteiger.
The goal was his first for his country in five years and made sure of a perfect start for Germany in their quest for a fourth European crown to match their four World Cup triumphs.
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