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Head's 16 boundaries in the powerplay was also a record, while he equalled Marcus Stoinis's Australian record for the fastest fifty in T20Is in 17 balls.
Hungary must wait to see whether they will qualify for the last 16 in one of the places reserved for the best four third-placed finishers.
Scotland kept alive hopes of reaching the knockout stages of a major tournament for the first time by holding Switzerland to a gripping 1-1 draw
Australia, who had already booked their spot in the second round, will have been disappointed with their fielding and the start of their innings but Travis Head (68) and Marcus Stoinis (59) accelerated in the last 10 overs to help get them across the line.
The Germans, hunting a record fourth European title and first major trophy after a barren decade, scored through Florian Wirtz, Jamal Musiala and a Kai Havertz penalty before Niclas Fuellkrug and Emre Can added two more late in the second half.
Walter, 35, is no stranger to predicting the outcome of football matches, and is a veteran of previous World Cup and Euros campaigns, as well as German and European club competitions.
While Australia are overwhelming favourites agaainst Scotland in their final group match on Saturday, Hazlewood said they would welcome a narrow win that would end England's title defence.
Germany have won four World Cups and three European Championships but their stellar tournament reputation has been somewhat tarnished with a series of failures since their 2014 World Cup victory in Brazil.
Defending champions England need to win their remaining games against Namibia and Oman by big margins to have any chance of progressing to the second round.
Captain Berrington made an unbeaten 47 from 35 balls and shared a 74-run fifth-wicket partnership with Leask (35 from 17) which steered Scotland to their first win over Namibia in four T20 internationals.
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