Hungary looked like they would shock their hosts and send them out of the tournament after Adam Szalai's diving header in the 11th minute to open the scoring.

Kai Havertz eventually drew Germany level in the 66th minute, only for Hungary to retake the lead seconds after the re-start as Andras Schaefer ran onto a pass and headed in.

Goretzka bagged the crucial equaliser in the 84th minute to send Germany through in second place behind France in Group F on four points.

The run-up to the game had been overshadowed by UEFA's refusal to allow the stadium to be lit in rainbow colours to oppose a Hungarian anti-LGBTQ law, and a protester waving a rainbow flag invaded the pitch ahead of kick-off.

It was all business for the hosts once the whistle was blown, however, as they were desperate to avoid a repeat of their shock 2018 first round World Cup exit, with Joshua Kimmich testing keeper Peter Gulacsi after three minutes.

But it was the Hungarians who then stunned the home crowd with Szalai's diving header on the break.

The Germans had close to 70 per cent possession in the first half and Mats Hummels hit the crossbar with a powerful header, but other than that they showed little of the attacking spark they demonstrated in their win over Portugal, who advanced to the last 16 with a 2-2 draw against France to finish third in the group.

Germany, who had never gone out at the group stage of consecutive major tournaments, showed nerves as their game gradually became more and more scrappy.

It was also a scrappy goal that brought them level, with Gulacsi failing to connect with a Kimmich free-kick, Hummels heading the ball on and Havertz nodding in.

But as the German fans celebrated in the stands, Hungary scored straight after the restart, with Szalai lofting the ball into the German half and Schaefer lunging forward and heading it past keeper Manuel Neuer.

With Hungary defending desperately to protect their spot in the knockout stages, Toni Kroos tried his luck from a tight angle but his effort flashed wide.

The German pressure finally paid off when substitute Jamal Musiala cut the ball in the box and fellow substitute Goretzka drilled it home to avoid another tournament fiasco for the Germans and set up a mouth-watering encounter with The Three Lions in London.

Euro 2020 Round of 16:

June 26: Wales v Denmark in Amsterdam; Italy v Austria in London

June 27: Netherlands v Czech Republic in Budapest; Belgium v Portugal in Seville

June 28: Croatia v Spain in Copenhagen; France v Switzerland in Bucharest

June 29: England v Germany in London; Sweden v Ukraine in Glasgow

Australian Associated Press