The Frenchman's best lap of one minute 26.929 enabled him to leapfrog the Ferrari duo of Fernando Alonso (1.27.000) and Felipe Massa (1.27.241) into top spot.
The dark storm clouds then swept across Albert Park and for 20 minutes, high winds and heavy rain kept the drivers off the track and no one was able to better Grosjean's time when the cars returned on wet weather tyres.
World champion Sebastian Vettel, who dominated both practice sessions for Red Bull in dry conditions on Friday, was only able to set the 12th best time and pulled off the track after the rain with a hydraulics problem.
Mark Webber, still seeking his first win at his home race at his 12th attempt, was just behind his German team-mate in 13th, although he was one of the quickest drivers on the wet track.
Grosjean also set the pace after the rain ahead of his team mate Kimi Raikkonen and the Saubers of Nico Hulkenberg and Esteban Gutierrez, who managed 20 laps despite the weather.
McLaren's Jenson Button complained over the team radio about understeer in his brief four-lap stint in the dry, indicating that the problems with his car exposed on Friday had not been resolved overnight.
Button, winner of the Melbourne race in three of the last four years and the final race of last season, was a whopping 2.4 seconds off the pace set by Vettel in second practice and he set the 17th quickest time in the third session.
His fellow Briton Paul Di Resta was fourth quickest on the timesheets ahead of Grosjean's team mate Kimi Raikkonen with Australian Toro Rosso driver Daniel Ricciardo sixth fastest before the rain descended.
Mercedes drivers Nico Rosberg and Lewis Hamilton failed to really get their sessions going and finished 11th and 22nd fastest respectively.
Vettel, embarking on his campaign to win a fourth straight world title this season, was hot favourite to claim pole position in qualifying for Sunday's race later on Saturday.