Highlights: Zverev looks ominous as he strolls past Bedene
He won the next eight games, and Bedene never recovered. It took Zverev one hour and 55 minutes to come through against former British player Bedene, who now competes for Slovenia. Zverev out-aced Bedene 11-7 and hit 35 winners compared to his opponent's 19.
German Zverev will play the winner of an all-French first round match between Jeremy Chardy and Ugo Humbert.
Zverev, known as Sascha, has emerged as the leader of tennis' new generation of men's players, a reputation confirmed late last year by his maiden ATP Finals triumph where he beat Roger Federer and Novak Djokovic in consecutive days to take the title.
The youngster, who also won three other tournaments in 2018, hasn't advanced beyond the third round in three previous trips to the Australian Open.