The triple world champion bossed the field and held a half-second gap over Ferrari's Sebastian Vettel and his new Mercedes team-mate Valtteri Bottas in the afternoon session.
Britain's Hamilton followed up his field-leading fastest lap of 1 minute, 24.220 secs in the morning run with a blistering 1:23.620 in the late afternoon.
It was around one-tenth of a second off Vettel's circuit record of 1:23.529, posted for Red Bull in qualifying ahead of his 2011 race victory.
"Hamilton is in a league of his own at the moment," Mercedes team boss Toto Wolff said.
"His one-lap pace was really good and he took the ultrasofts for 17 laps and was stable. I'm happy."
Ferrari was expected to press Hamilton and the Mercedes team after superior times in pre-season testing, but on the evidence of the opening two sessions Hamilton is again the driver to beat in Sunday's season-opener.
"I'm super-happy to be back in the car, particularly after a first day like that. It was 99 percent perfect," Hamilton said.
"We've shown good form so far on both the long and short runs and we got every lap done that we wanted to. The tyres performed really well today too.
"I'll be pushing as hard as I can to win this race."
Hamilton's time was more than three seconds faster than his best lap in last year's corresponding free practice in Melbourne.
Finland's Bottas slotted smoothly into the Mercedes team environment with a best lap of 1:24.176.
"I definitely feel like I can make a step forward tomorrow. It'll be a busy evening for us looking through all the data to see where we can improve, but it's a reasonable start," Bottas said.
Pole 'may be a stretch' for Ferrari
Ferrari improved markedly on their opening practice, with Vettel unleashing the second best lap time in FP2 with 1:24.167 while team-mate Kimi Raikkonen was fourth with 1:24.525. "We (were) very happy at testing – times looked good, but here is where it matters," Vettel said.
"The car hasn't changed much and it's good to be back but we can still improve."
The Red Bulls of Daniel Ricciardo and Max Verstappen were over a second behind Hamilton and half-a-second off Vettel's Ferrari.
"We can still get more out of it. This morning was promising but we tried a few things this afternoon and they didn't work as much as we'd like," said Ricciardo, bidding to become the race's first Aussie winner in 37 years.
"Mercedes sure are quick but it's more Lewis than Valtteri. I think we can be up there. Pole (position) may be a stretch but we're in that next little group."
Verstappen missed out on the later long runs after damaging his car's floor when running over the gravel on the exit of turn 10.
"I had a bit of understeer, so went off the track and damaged the floor," Verstappen said. "We tried to find a better balance and we are just a bit too slow. We are where I expected us to be."
The second session was stopped after a big crash for Renault's Jolyon Palmer, who lost the rear of his car on the last corner and spun into the barriers.
"I'm fine," Palmer told his team over the radio. The shunt damaged the car's rear suspension, while the rear wing was detached.
Palmer missed the remainder of the session, in a blow to his preparations for the weekend race.
Brazilian Felipe Massa stopped his Williams car at Turn 11 after reporting he could not engage gears, and walked back to the team garage.
The troubled McLaren team had no on-track breakdowns on the opening day with Fernando Alonso finishing in a respectable 12th place.
RESULTS – SECOND PRACTICE
1. Lewis Hamilton (Britain) Mercedes 1:23.620
2. Sebastian Vettel (Germany) Ferrari 1:24.167
3. Valtteri Bottas (Finland) Mercedes 1:24.176
4. Kimi Raikkonen (Finland) Ferrari 1:24.525
5. Daniel Ricciardo (Australia) Red Bull 1:24.650
6. Max Verstappen (Netherlands) Red Bull 1:25.013
7. Carlos Sainz (Spain) Toro Rosso 1:25.084
8. Romain Grosjean (France) Haas 1:25.436
9. Nico Hulkenberg (Germany) Renault 1:25.478
10. Daniil Kvyat (Russia) Toro Rosso 1:25.493
11. Sergio Perez (Mexico) Force India 1:25.591
12. Fernando Alonso (Spain) McLaren 1:26.000
13. Esteban Ocon (France) Force India 1:26.145
14. Felipe Massa (Brazil) Williams 1:26.331
15. Marcus Ericsson (Sweden) Sauber 1:26.498
16. Lance Stroll (Canada) Williams 1:26.525
17. Stoffel Vandoorne (Belgium) McLaren 1:26.608
18. Pascal Wehrlein (Germany) Sauber 1:26.919
19. Kevin Magnussen (Denmark) Haas 1:27.279
20. Jolyon Palmer (Britain) Renault 1:27.549
RESULTS – FIRST PRACTICE
2 Valtteri Bottas (Finland) Mercedes – 1:24.803
3 Daniel Ricciardo (Australia) Red Bull – 1:24.886\
4 Max Verstappen (Netherlands) Red Bull – 1:25.246
5 Kimi Raikkonen (Finland) Ferrari – 1:25.372
6 Sebastian Vettel (Germany) Ferrari – 1:25.464
7 Felipe Massa (Brazil) Williams – 1 1:26.142
8 Romain Grosjean (France) Haas – 1:26.168
9 Nico Hulkenberg (Germany) Renault – 1:26.183
10 Sergio Perez (Mexico) Force India – 1:26.276
11 Carlos Sainz (Spain) Toro Rosso – 1:26.450
12 Daniil Kvyat (Russia) Toro Rosso – 1:26.514
13 Lance Stroll (Canada) Williams – 1:26.734
14 Fernando Alonso (Spain) McLaren – 1:27.116
15 Marcus Ericsson (Sweden) Sauber – 1:27.348
16 Esteban Ocon (France) Force India – 1:27.656
17 Kevin Magnussen (Denmark) Haas – 1:27.667
18 Pascal Wehrlein (Germany) Sauber – 1:28.539
19 Jolyon Palmer (Britain) Renault 1:28.585
20 Stoffel Vandoorne (Belgium) McLaren 1:28.695