Sebastian Vettel was 0.873secs back in fifth spot in the second session and Hamilton was encouraged by the performance of the W10 as he eyes a winning start at Albert Park on Sunday.
Lewis Hamilton, with a 1m 22.600s, bested teammate Valtteri Bottas by just 0.048 seconds with the red-marked soft tyre, but such was the Briton and his team's superiority that even his lap on the slower medium-compound rubber would've been enough to have him lead the session.
Verstappen's attacking style and sheer pace has seen him long tipped to become a future world champion and Red Bull showed their faith with a contract that pays him only less than multiple-time world champions Hamilton and Vettel and the bumper deal Ricciardo signed with Renault.
Sebastian Vettel, who has won in Melbourne for the past two years, could only manage fifth, almost a second adrift of arch-rival Hamilton, while Ferrari partner Charles Leclerc struggled to ninth, straddling the kerb and spinning as he pushed hard late in the day.
Alfa Romeo newcomer Kimi Raikkonen was sixth fastest, a tenth behind Vettel, and just ahead of the two Renaults of Nico Hulkenberg and Daniel Ricciardo.
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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.
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.
"We still have lots to learn and improve on, but we're getting there". Are the red cars keeping something in reserve for qualifying and the race?
The other rookie in the field - 2018 Formula 2 champion George Russell - also had an off when he ran wide at Turn 4 late in the session and had to recover through the gravel, on what was a chastening day for Williams. Not so much in terms of lap time but more in terms of auto feel and handling. "We didn't really get into the groove and the rhythm".
"We finally got some laps in".
It was a tricky second session for the inexperienced drivers, with Alexander Albon again making errors after his crash in FP1. "It's not too dissimilar to how it was a year ago driving round here". He reiterated that Mercedes had plenty of "work to do" in Thursday's media conference.