Germany have never exited consecutive major tournaments at the group stage but need at least a draw against Hungary to be sure of avoiding that fate.
Joachim Low's side suffered an awful early elimination at the 2018 World Cup and were facing further pain after losing their Euro 2020 opener against France.
The 2014 world champions recovered with a stunning 4-2 win over holders Portugal, though, and could yet top the group with a win, setting up a meeting with a third-placed finisher.
But Germany face a highly motivated Hungary side, who will themselves make the last 16 with a win after drawing at home to France.
The only previous occasion on which the teams met in the group stage saw Germany fall to a record defeat, 8-3 at World Cup 1954. They did recover to beat Hungary in the final, however.
And the Magyars have not won their final group match since the 1966 World Cup.
Marco Rossi acknowledges the odds are stacked against his side, describing simply qualifying for the tournament as a "major achievement" on the eve of the match.
"We play against three teams that may get to the semi-finals and play in London," he said.
"Our group has been called a 'Group of Death' and evidently the one to fall there is Hungary. In theory, it's hard to disagree with someone making such a prediction."
PLAYERS TO WATCH
Germany – Kai Havertz
Chelsea team-mate Timo Werner has so far been kept on the fringes, but Havertz became Germany's youngest ever European Championship scorer at 22 years and eight days old against Portugal. Only three younger players – Thomas Muller (20 in 2010), Franz Beckenbauer (20 in 1966) and Lukas Podolski (21 in 2006) – have scored in consecutive tournament games for Germany, as Havertz could.
Hungary – Roland Sallai
Hungary have only scored once so far at this tournament, but Sallai assisted Attila Fiola's strike against France and is suddenly a man in form for his country. Sallai has also scored twice in his past four international appearances, his three goal involvements as many as in his first 20 games for Hungary.
KEY OPTA FACTS
– Germany and Hungary's only previous meeting in Munich was 110 years ago, in a friendly played in December 1911 at the city's MTV-Platz stadium. Hungary won 4-1.
– Under Joachim Low, Germany have beaten Hungary both times they have met – both friendlies, by an aggregate scoreline of 5-0 (3-0 in Budapest in 2010, 2-0 in Gelsenkirchen in 2016).
– Hungary are without a win in each of their past five matches at the European Championship (D3 L2) since a 2-0 victory against Austria in 2016. Indeed, that 2-0 win versus Austria is their only clean sheet in their 10 matches in the competition.
– Against Portugal last time out, Germany's four goals took them to 302 scored overall in major tournaments (World Cup and Euros); indeed, no other European nation have yet reached 200 such goals (France 184 next highest).
– Fiola has scored two goals in his past four appearances for Hungary, after failing to score in his first 33 games for his country. Indeed, Fiola (31y, 122d) is the second-oldest player to score for Hungary at the European Championship after Zoltan Gera (37y 61d) against Portugal at Euro 2016.