Max Verstappen was third fastest for Red Bull-Honda, eight tenths slower than Hamilton, after opting to delay his performance run to the closing stages of the session.
Ferrari was off the pace the second time around, with two-time defending Australian GP champion Vettel in fifth spot and Leclerc sliding backward into the track-side grass after losing control with only minutes remaining and recording the ninth-fastest lap.
Meanwhile, the Mercedes and Ferrari drivers have said they will be able to race with, and against, their team-mates - despite the new team principal of the Italian outfit suggesting they would favour Vettel over Charles Leclerc in certain situations.
Ferrari, who appeared to have the quickest vehicle in pre-season testing, were fourth with Sebastian Vettel.
The 39-year-old Kimi Raikonen was sixth in his first start since leaving Ferrari for Alfa Romeo Racing, and the Renault pair of Nico Hulkenberg and Daniel Ricciardo were next.
The first day of running for the 2019 Formula One season is in the books, and after four months without a race the opening day of practice raised nearly as many questions as it answered.More news: Two rockets fired from Gaza at Tel Aviv area, says Israeli army
"They've shown good reliability in pre-season testing which tells you they can turn the engine up a bit more perhaps".
"We got through our program really well, no issues on track".
"By the time you finish the testing, the cars are ready to be shipped directly to Melbourne, so I think it's really by here that we start understanding who is the fastest". "They are still the team to beat - we are just trying to improve and go as fast as we can".
There was some speculation in the paddock that Ferrari may have been sandbagging, or deliberately holding back ahead of qualifying on Saturday.
Meanwhile, Mercedes boss Toto Wolff has said Hamilton's activities outside of Formula One - skydiving and his fashion brand - were not a "negative distraction".
"It was a tricky day for us".
British-born Thai debutant Alexander Albon had a tough day, crashing his Toro Rosso to lose his front wing and cause a brief halt in the first session. So for Raikkonen to be that close in a auto that will undoubtedly be slower only emphasised the point that Ferrari can find plenty more time. "It's not too dissimilar to how it was previous year driving round here".