With the thermometer peaking at a stifling 40 degrees Celsius (104 F), the 20-year-old fourth seed was grateful for the relative cool of the evening and looked set for an early bed-time as he raced through the opening two sets under the lights at Hisense Arena.
That was until 62nd-ranked Gojowczyk rallied to break Zverev in the third game of the third set and held the advantage bravely to make a game of the contest.
Chastened, Zverev knuckled down to deny his opponent a look at his serve in the final stanza and sealed the match with an ace to set up a clash with fellow 'Next Gen' member Chung Hyeon of South Korea for a place in the final 16.
"I think I played a pretty good match," the straggly-haired Zverev told reporters after his nearly two-hour battle.
"I think the third set I played maybe a little bit shorter, maybe a little bit more passive.
"I don't think I played a very good set. I just feel like Peter played an amazing 25 minutes of tennis, then the set was gone."
Zverev has matched his best result in Melbourne, having also made the third round last year where he was beaten by Rafa Nadal in a five-set classic.
Having collected five titles in a brilliant 2017 season, he is seen among the best-placed of the young brigade to upset the grand slam cartel of Roger Federer and Rafa Nadal, despite having never passed the fourth round of the majors.
Breaking through for a maiden quarter-final would be well earned in Melbourne, with six-times champion Novak Djokovic looming as a possible fourth round challenge.
(Editing by Catherine Evans)
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