The 22-year-old latched onto a through-ball from Liverpool’s Emre Can to slot home, before tucking away a 25-yard free-kick just after half time.
Borussia Dortmund’s young centre-back Matthias Ginter then headed home a third just a few minutes later to put Germany top of the group on four points.
The Germans now only need a draw to progress when they face hosts Czech Republic on Tuesday, who bounced back from their opening defeat to the Danes to thrash Serbia 4-0 earlier in the evening.
Jan Kliment broke the deadlock with a close-range finish with less than eight minutes on the clock, then capitalised on a Serbian keeper’s parry to double their lead 13 minutes later.
He then completed his hat-trick 10 minutes after half time, before Martin Frydek volleyed home their fourth just before the hour.
Serbia will now need victory over Denmark in their final group game to have any chance of qualifying for the last four.