Alfa Romeo's Kimi Raikkonen was fifth quickest - just 0.099secs behind his former Ferrari team-mate Vettel.
His team mate Nico Hulkenberg was left confined to the garage for most of the session as engineers worked on an electrical problem but the German later emerged to clock the 10th fastest lap.
"Of course, I'm always anxious and we had a laugh a year ago because I couldn't get hold of him or my chief strategist or one of the race engineers because they were racing motorbikes", he said.
Vettel found his vehicle behaving a bit differently than it did in the pre-season winter testing.
Following the regulation changes over the winter that affect the front and rear wings and the bargeboards, pre-season testing indicated that the so-called "Class B" outfits, whom Renault is hoping to pull clear of in 2019, had universally closed the gap to the leading trio. Hulkenberg spent more than an hour of his morning session with his vehicle on jacks in the garage with an electronics issue, while new teammate Ricciardo lost nearly 30 minutes of his afternoon to a technical problem before taking to the track, though both ended up in the mix at the head of the midfield as expected by the end of the day. "There's plenty of things we can improve on, which is a positive, but it's absolutely not a bad start at all".
Charles LeClerc, the second youngest driver for Ferrari in history, was only just a brush off the top spot, lapping +0.074 behind Hamilton.
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"We didn't bring a lot of new parts to the auto, but we were able to optimise the package that we have". The forecast is for warmer conditions for Saturday's qualifying and Sunday's race.
Vettel slid onto the grass at turn one early in the afternoon run.
Meanwhile, Mercedes boss Toto Wolff has said Hamilton's activities outside of Formula One - skydiving and his fashion brand - were not a "negative distraction". I think we simply focused on ourselves, we had eight intense days, very little time to prepare for Melbourne. "Box", he said on the team radio.
"If we can get that confidence and that groove back, there is a lot of lap time in that around here", he added.
It was a tricky second session for the inexperienced drivers, with Alexander Albon again making errors after his crash in FP1.
His best time of 1:26.655 for Williams was slowest on a day marred by the sudden death on Thursday of long-serving and well-respected Formula One race director Charlie Whiting.