Liuzzi, last year's Formula 3000 champion who could replace Austrian Christian Klien as a race driver later in the year, did his reputation no harm as teams limbered up on Friday for Sunday's season-opener.
He was the only driver to lap the Albert Park circuit in under one minute 26 seconds.
Liuzzi was also one of just a handful to do more than 10 laps due to new regulations forcing drivers to make their engines last for two race weekends.
Ferrari's seven times world champion Michael Schumacher did not complete a timed lap and neither did either of the much-fancied Renault drivers or McLaren's title contender Kimi Raikkonen.
Brazilian Rubens Barrichello, Schumacher's team mate, completed five laps in Ferrari's modified version of last year's F2004 car.
The three quickest times were all produced by test drivers who will not race on Sunday.
Liuzzi did 19 laps, with a best of 1:25.967, with Spaniard Pedro de la Rosa second fastest for McLaren and Brazilian Ricardo Zonta third for Toyota.
Colombian Juan Pablo Montoya, in a McLaren, was fourth while Liuzzi's team mate David Coulthard confirmed Red Bull as a team to watch with the fifth best time.
The team has replaced Jaguar Racing, bought by Austrian energy drink billionaire Dietrich Mateschitz in November.
Minardi did not take part in the session after failing to secure the agreement of all the teams to allow them to run with last year's unmodified car.
Team boss Paul Stoddart, who comes from Melbourne, was still hoping to persuade Ferrari's Jean Todt to change his mind and allow the regular tail-enders to run.
Canadian former world champion Jacques Villeneuve, who took pole position in the first race at Albert Park 10 years ago, was first out on track in his Sauber.
India's Narain Karthikeyan made his debut at a grand prix weekend in a Jordan but returned to the garage with a smoking Toyota engine after six laps.