The Briton topped the morning by half a second over world champion Sebastian Vettel's Red Bull, with the two Mercedes next up. Melbourne winner Jenson Button was hampered by an oil leak and was back in ninth for McLaren.
Although forecasts of rain later encouraged teams to complete plenty of mileage this morning, it was still half an hour into the session before serious times were set, with Kimi Raikkonen and Michael Schumacher leading briefly for Lotus and Mercedes respectively before Hamilton and Vettel began a battle for first place.
A 1m38.598s put the McLaren in front after 34 minutes, but only for two minutes before Vettel beat it by 0.063 seconds.
Hamilton narrowly missed out on reclaimed first place with his next lap, before putting in the 1m38.021s that would keep him ahead for the rest of the session.
Behind Vettel, Nico Rosberg narrowly beat Mercedes team-mate Schumacher to third.
Romain Grosjean took fifth for Lotus despite pitting for checks early on after reporting a strange feeling at the rear of the car.
Mark Webber completed the top six in the second Red Bull, ahead of Raikkonen, with Paul di Resta and Nico Hulkenberg's Force Indias eighth and 10th.
Button managed to complete 15 laps before the issue that left his McLaren parked in the garage for the final part of the session.
Williams test driver Valtteri Bottas made his debut in an official session with 11th place, 0.059s quicker than team-mate Pastor Maldonado.
Ferrari was back in 13th and 15th with Felipe Massa and Fernando Alonso.
Problems continued for HRT, as Narain Kartikeyan parked on track with gearbox issues after eight laps, and Pedro de la Rosa was 7.5s off the pace at the back of the pack.
Pos Driver Team Time Laps 1. Lewis Hamilton McLaren-Mercedes 1m38.021s 19 2. Sebastian Vettel Red Bull-Renault 1m38.535s + 0.514 21 3. Nico Rosberg Mercedes 1m38.813s + 0.792 21 4. Michael Schumacher Mercedes 1m38.826s + 0.805 19 5. Romain Grosjean Lotus-Renault 1m38.919s + 0.898 17 6. Mark Webber Red Bull-Renault 1m39.092s + 1.071 20 7. Kimi Raikkonen Lotus-Renault 1m39.128s + 1.107 22 8. Paul di Resta Force India-Mercedes 1m39.298s + 1.277 23 9. Jenson Button McLaren-Mercedes 1m39.323s + 1.302 15 10. Nico Hulkenberg Force India-Mercedes 1m39.440s + 1.419 19 11. Valterri Bottas Williams-Renault 1m39.724s + 1.703 23 12. Pastor Maldonado Williams-Renault 1m39.783s + 1.762 23 13. Felipe Massa Ferrari 1m39.896s + 1.875 16 14. Kamui Kobayashi Sauber-Ferrari 1m39.910s + 1.889 21 15. Fernando Alonso Ferrari 1m39.980s + 1.959 23 16. Jean-Eric Vergne Toro Rosso-Ferrari 1m40.099s + 2.078 23 17. Heikki Kovalainen Caterham-Renault 1m40.247s + 2.226 19 18. Daniel Ricciardo Toro Rosso-Ferrari 1m40.469s + 2.448 23 19. Vitaly Petrov Caterham-Renault 1m40.857s + 2.836 25 20. Sergio Perez Sauber-Ferrari 1m41.085s + 3.064 23 21. Timo Glock Marussia-Cosworth 1m43.170s + 5.149 18 22. Charles Pic Marussia-Cosworth 1m44.580s + 6.559 14 23. Narain Karthikeyan HRT-Cosworth 1m45.360s + 7.339 8 24. Pedro de la Rosa HRT-Cosworth 1m45.528s + 7.507 18 All Timing Unofficial