Piastri logged the 12th quickest lap of the 20 drivers in his debut F1 appearance in his home city on Friday.
Reigning world champion Verstappen set the pace followed by Mercedes ace Lewis Hamilton and Red Bull's Sergio Perez.
Verstappen and Perez entered Melbourne after finishing one-two in the opening races of the season in Bahrain and Saudi Arabia.
Verstappen won the season-opener and finished second behind Perez in the next race.
Verstappen logged the quickest time of one minute 18.790 seconds before spinning out late in the hour-long session.
Hamilton (1:19.223), Perez (1:19.293), Aston Martin's Fernando Alonso (1:19.317) and Ferrari's Charles Leclerc (1.19.378) were next best.
Melbourne-born Piastri recorded a fastest time of 1:19.777 from his 22 laps in a practice session halted midway for five minutes due to a GPS issue.
The session also prematurely ended with four minutes remaining in the scheduled hour when Logan Sargeant's Williams lost power and was parked on a corner.
A second practice session will commence at 4pm AEDT.
A third and final practice will be held on Saturday before the qualifying session for Sunday's race.
Verstappen (44 points) leads the championship by one point from Perez followed by Alonso (30 points), with Ferrari's Carlos Sainz and Hamilton both on 20 points.
AAP
