The Serbian great is on his latest mission to win a record 25th Grand Slam title and dismissed the Italian 6-3, 6-2, 6-2.
Djokovic faces China’s Shang Juncheng or Botic van de Zandschulp of the Netherlands next in Melbourne.
Djokovic is well known for his sometimes unusual preparations, which include hugging a Brazilian fig tree in Melbourne’s botanical gardens.
“That is my oldest friend here in Melbourne,” said the 38-year-old former world number one, who has won 10 Australian titles, more than anyone in history.
“He has been there to heal my wounds and give me company.
“It’s a beautiful connection, nature is such a powerful ally.
“We have a friendship going over 20 years.”
In sunny, but noticeably cooler temperatures than recent days, the fourth seed appeared determined to get the job done as fast as possible.
Playing in the early afternoon on Rod Laver Arena, rather than his usual evening slot, Djokovic raced into a 5-2 lead.
The Italian doggedly held serve despite facing multiple set points, but it was only delaying the inevitable as Djokovic sealed the opening set in 47 minutes.
Djokovic, who has been tied with Margaret Court on 24 major titles since winning the US Open in 2023, was not quite as devastating as when winning his first-round match by the same scoreline.
But he still had far too much for the outclassed 23-year-old.
Djokovic broke Maestrelli, who was making his Grand Slam debut, to start the second set and cantered into the third round.
Keys draws on champion mindset
Madison Keys said she drew on her experience as defending champion to pull through a danger moment and make the Australian Open third round on Thursday, rattling off five straight games to secure victory.
Keys, who upset Aryna Sabalenka in last year’s final, blew hot and cold against fellow American Ashlyn Krueger before getting over the line 6-1, 7-5.
It set up a clash with former semi-finalist Karolina Pliskova after the Czech ended the dreams of Indonesia’s Janice Tjen in straight sets.
“I think in those tough kind of moments like today, getting down in that second set, just kind of reminding yourself that you have been here before, you figured it out,” Keys said.
“I think when you’re able to do that in a place where you have had success, it just feels like it comes a little bit easier.”
Keys admitted after her laboured first-round win that she was a bundle of nerves and “too timid”.
The 29-year-old threw off the shackles in the first set against the 92nd-ranked Krueger, taking it in just 23 minutes on John Cain Arena before having to rally from 2-5 down in the second.
“I started really well and Ash a little slowly,” said Keys, who began her season with quarter-final exits at Brisbane and Adelaide.
“I fully expected her to raise her level and she did. But it just got away from me a little quickly.
“Then once I got that momentum (back), I just tried to sink my teeth into the set and do whatever I could to get back into it.”
After taking more than an hour to win the first set in her opening round, Keys broke on three occasions against Krueger to storm through it this time.
Hitting well and pushing her opponent around the court, the ninth seed looked ominous and held to love in opening her second set account.
But Krueger, consulting a book at the changeovers, upped her intensity and against the odds broke Keys to lead 3-2 after the champion’s serve imploded, double-faulting three times.
Keys was broken again, to love and once more on a double-fault, to slump 5-2 behind.
However, she gathered herself to reel off five straight games and stay in the title hunt.