The Briton posted a lap of one minute 25.624 seconds, 0.176 seconds ahead of team mate Nico Rosberg at Melbourne's Albert Park circuit.
Four-times world champion Sebastian Vettel was third quickest for Ferrari, just over two-tenths of a second adrift of Hamilton, with Toro Rosso's Carlos Sainz fourth.
After both of Friday's practice sessions were plagued by rain showers, all 22 cars made it out onto a dry track on a sunny day to post laps but the more favourable conditions failed to prevent mishaps.
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Indonesian rookie Rio Haryanto got off to a rough start when he rolled out of the Manor Racing garage and straight into Romain Grosjean's Haas in the pit-lane.
Frenchman Grosjean needed to have his floor and front wing replaced before he re-emerged midway through the session to finish 19th.
Haryanto, his nation's first Formula One driver, had the slowest lap, more than three seconds off Hamilton's best.
Former world champion Kimi Raikkonen was fifth fastest in the session, with Toro Rosso's teenage prospect Max Verstappen sixth.
Daniel Ricciardo was the quicker of the Red Bulls with the eighth-best time, while McLaren's Fernando Alonso's was 11th quickest, one ahead of team mate Jenson Button.
(Editing by John O'Brien)
