Sebastian Vettel's session ending spin meant that he was unable to get any running on the soft compound Pirellis before qualifying. AFP
Grosjean was second fastest ahead of local hero Mark Webber of Red Bull and Briton Jenson Button in the second McLaren.
German Nico Rosberg was fifth, ahead of his Mercedes team-mate and compatriot Michael Schumacher. Another German, defending double champion Vettel of Red Bull, was back in a disappointing seventh.
Both Vettel and Schumacher spun off the circuit in the closing stages of the hour-long session, beaching their cars in gravel traps.
McLaren team chief Martin Whitmarsh said: "It's nice to be fastest, again, but really it does not mean anything. It looks tight and very close. We think we are competitive, but so are Mercedes and Red Bull, and maybe Lotus too."
Venezuelan Pastor Maldonado of Williams was eighth ahead of Mexican Sergio Perez of Sauber, with Australia's second entrant Daniel Ricciardo taking 10th for Toro Rosso.
Returning 2007 champion Finn Kimi Raikkonen was 12th in the second Lotus, two-time champion Fernando Alonso was again off the pace in his Ferrari, as was team-mate Felipe Massa, down in 18th.
On a bright, dry and sunny day at Albert Park, with the air temperature rising to 23 degrees Celsius and the track temperature at 34 degrees, there was none of the capricious weather, or the humidity, of the previous few days.
Rosberg was the first man to clock a competitive time and initially he topped the lists before Hamilton and then Schumacher overhauled his effort.
The German then swept back to the top with a lap in 1:25.929 after 35 minutes of the hour, shortly before Vettel lost control -- and the rear end of his car -- at turn six.
His Red Bull was left in the gravel and out of action for the rest of the session.
Earlier, Felipe Massa had supplied the first spin of the day and Bruno Senna had recovered after running off the circuit at turn five.
Vettel's embarrassment was eased somewhat when Schumacher went off at turn nine, the entry to the Clark chicane, just seconds after Grosjean, on his Albert Park debut, clocked the then fastest lap with 1:25.758.
It was a dazzling effort by the winner of last year's GP2 title, but not quite good enough as Hamilton responded in the final seconds to top the lists.