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 one of the four best third-place finishers.
Hungary put up a fight but the hosts had too much quality in the final third, with Musiala firing in the opener midway through the first half after captain Gundogan refused to give up a lost cause in the box.
The Hungarians had an equaliser ruled out for offside just before the break, and Germany doubled their lead on 67 minutes as Gundogan swept home an assist by Maximilian Mittelstaedt.
Germany's recent struggles appear to be a thing of the past, and they 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 to the last 16 now hang by a thread, while group rivals Switzerland and Scotland meet in Wednesday's late match in Cologne.
Switzerland, quarter-finalists at Euro 2020, will be through to the last 16 with a win in that game.
Scotland are aiming to win a match at a major tournament for the first time since beating the Swiss 1-0 at Euro 96.
Gjasula saves Albania
Elsewhere on Wednesday, Albania's Klaus Gjasula scored at both ends, including a dramatic injury-time equaliser as his side drew 2-2 with Croatia in Hamburg.
After a disappointing 3-0 loss to Spain in their opening game in Group B, Croatia were behind again when Qazim Laci gave Albania an early lead.
But Croatia improved after the break and Andrej Kramaric levelled with 16 minutes remaining, before Gjasula put through his own net.
The Albania midfielder became the last-gasp hero, though, slotting into the bottom corner in the fifth minute of injury time to snatch his team a point.
Croatia, World Cup semi-finalists in 2022, will now likely need to win their final Group B match against holders Italy on June 24 to reach the knockout phase for a fifth straight major tournament.
"We will believe until the very end, to give our best as we did in this match," said forward Kramaric.
"Unfortunately we didn't win but we hope to be a bit luckier against Italy."
Albania have won plenty of plaudits with their performances against both Italy, in a 2-1 defeat, and Croatia, but could not hold a lead in either game and will probably have to beat Spain to keep their last-16 hopes alive.
"We have to go forward but we have to fight for every single point," said Albania's Brazilian coach, Sylvinho.
"It's important for our lives, the life of the country, the federation. I'm proud of the players so we have to enjoy the moment."
Group rivals Spain and Italy meet in Gelsenkirchen in the standout tie on Thursday, while England face Denmark and Slovenia take on Serbia in Group C.
