Two-time Grand Slam finalist Zverev is one of the biggest servers in the game and it was little surprise that Fearnley, despite being a sharp returner, could not initially get into his opponent’s service games.
There was little difference between the pair in a tight first set and Fearnley losing his serve to love in the sixth game was decisive.
A worrying sign was Fearnley gingerly moving between points towards the end of the set with what looked to be a lower back issue.
After Zverev secured the lead, Fearnley disappeared off court for a medical time-out and he returned looking more at ease.
Zverev, who reached the Melbourne semi-finals in 2021 and 2024, had not dropped serve in his opening wins over France’s Lucas Pouille and Spain’s Pedro Martinez.
Fearnley superbly took his serve once in each set – both as Zverev looked to consolidate breaking the Scot – but lapses of concentration saw him immediately lose serve again.
Zverev, 27, closed each set confidently to set up a last-16 meeting with one of two Frenchman, either 14th seed Ugo Humbert or 20th seed Arthur Fils.
“Jacob is an incredible player, he went through all the stages – going to university, playing Futures, Challengers – and now he is playing on the big stage,” said Zverev.
“I have massive respect for him. He will get better over the next few years.”
