Germany followed up their 5-1 demolition of Scotland in the tournament's opening game by seeing off the Hungarians in Stuttgart, with Jamal Musiala and Ilkay Gundogan scoring either side of half-time.
Julian Nagelsmann's team have a maximum six points with one game still to come in Group A, and are certain to progress to the last 16 at least as runners-up in the section.
Hungary put up a fight but the hosts had too much quality in the final third, with Bayern Munich star Musiala firing in the opener midway through the first half after captain Gundogan refused to give up a lost cause in the box.
Germany then doubled their lead on 67 minutes as Gundogan, of Barcelona, swept home an assist by Maximilian Mittelstaedt.
Their recent struggles appear to be a thing of the past, and Germany have now won their opening two games at a World Cup or European Championship for the first time since Euro 2012.
"We were determined to win today and confirm our performance against Scotland," said goalkeeper Manuel Neuer.
"We were dominant and deserved to win. You could see the euphoria in the stadium."
Hungary's hopes of progressing now hang by a thread, while group rivals Switzerland and Scotland played out a 1-1 stalemate in Wednesday's late match in Cologne.
Euro 2024: Hosts Germany through to last 16, draws for Scotland and Croatia
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