World champion Sebastian Vettel, however, had his session cut 15 minutes short when he got his Red Bull stuck in the trackside gravel after spinning off the track at turn six.
Former world champion Hamilton found his best lap of one minute 25.681 seconds late in the one-hour session to knock Frenchman Grosjean off the top of the timesheets by just 0.077 seconds in bright sunshine at Albert Park.
Grosjean, who is partnered by returning former champion Kimi Raikonnen at the former Renault team, was quick enough to hold off experienced Australian Mark Webber, who had a best lap of 1.25.900 in his Red Bull.
Hamilton's team mate and fellow Briton Jenson Button, who won back-to-back in Melbourne in 2009 and 2010, was fourth quickest in 1.25.906 with German Nico Rosberg (1.25.929) just behind in fifth.
After rain affected both practice sessions on Friday, this was the first chance for the cars to try out their dry set-ups for any length of time and it was the Mercedes of Rosberg and Michael Schumacher who set the early pace.
Schumacher, the seven-times world champion, also ended having his car lifted out of the gravel, however, after losing control at the ninth corner late into the session. He set the sixth quickest time in 1.26.078.
Vettel, who claimed a record 15 pole positions including on his way to victory at Albert Park last season, was seventh fastest before his "off" in 1.26.211.
Ferrari's problems continued in an uncompetitive session where twice champion Fernando Alonso and Felipe Massa were only able to record the 16th and 18th fastest times.
HRT drivers Pedro de la Rosa and Narain Karthikeyan look unlikely to qualify for the race with best laps around 7.5 seconds off the lead, well outside the 107 percent they will require to take their place on the grid.
Qualifying for Sunday's race takes place later on Saturday.
1. Lewis Hamilton (Britain) McLaren 1:25.681
2. Romain Grosjean (France) Lotus - Renault 1:25.758
3. Mark Webber (Australia) RedBull - Renault 1:25.900
4. Jenson Button (Britain) McLaren 1:25.906
5. Nico Rosberg (Germany) Mercedes 1:25.929
6. Michael Schumacher (Germany) Mercedes 1:26.078
7. Sebastian Vettel (Germany) RedBull - Renault 1:26.211
8. Pastor Maldonado (Venezuela) Williams - Renault 1:26.470
9. Sergio Perez (Mexico) Sauber - Ferrari 1:26.632
10. Daniel Ricciardo (Australia) Toro Rosso 1:26.723
11. Jean-Eric Vergne (France) Toro Rosso 1:26.733
12. Kimi Raikkonen (Finland) Lotus - Renault 1:26.737
13. Kamui Kobayashi (Japan) Sauber - Ferrari 1:26.755
14. Nico Huelkenberg (Germany) Force India 1:27.029
15. Bruno Senna (Brazil) Williams - Renault 1:27.119
16. Fernando Alonso (Spain) Ferrari 1:27.323
17. Paul Di Resta (Britain) Force India 1:27.428
18. Felipe Massa (Brazil) Ferrari 1:28.023
19. Heikki Kovalainen (Finland) Caterham - Renault 1:28.341
20. Vitaly Petrov (Russia) Caterham - Renault 1:28.702
21. Timo Glock (Germany) Marussia - Cosworth 1:30.728
22. Charles Pic (France) Marussia - Cosworth 1:31.225
23. Pedro de la Rosa (Spain) HRT - Cosworth 1:33.114
24. Narain Karthikeyan (India) HRT - Cosworth 1:33.261