Hometown hero Piastri lapped Albert Park in one minute, 19.729 seconds on a sunny afternoon, 0.214 seconds ahead of Mercedes drivers Kimi Antonelli and George Russell.
Piastri ran sixth quickest with a compromised run plan in the first practice (FP1) session after being hit with power unit calibration issues before completing a lap.
"There are just so many things to get to grips with," he said of F1's new engine era.
"It’s very different to what we had last year, but I think FP2 as a session was pretty smooth."
McLaren teammate and defending champion Lando Norris also suffered reliability issues, with a transmission problem costing him lap-time in FP1.
He placed seventh in FP2 after being 19th in FP1.
Ferrari's Lewis Hamilton was fourth quickest in FP2 ahead of fifth-placed teammate Charles Leclerc, who topped the first practice (FP1) in 1:20.267.
Minor pit lane drama
The new hybrid engines, which feature a much larger share of electric power than in the previous era, have proved a steep learning curve for drivers, placing a greater onus on managing energy deployment and regeneration.
The virtual safety car was triggered twice in FP1, and the mishaps continued in FP2, with immediate drama in the pit lane.
Russell needed a minor fix to the front of his car after colliding with Racing Bulls' 18-year-old rookie Arvid Lindblad when pulling out of the garage.
"This guy's just hit my front wing," Russell said over the team radio.
Both drivers were set to face stewards.
Alpine's Franco Colapinto will also be investigated for abruptly slowing in the pit lane, forcing Hamilton to swerve.
Max Verstappen stalled in the pit lane straight after exiting the Red Bull garage, and later took a heavy skid through gravel after locking up at turn 10.
The four-time champion and last year's runner-up sat out nearly half the session before returning to post the sixth-fastest time.
Lindblad, the sole debutant starting the season and youngest-ever British F1 racer, impressed with his poise.
He was fifth quickest in FP1 and eighth in FP2, putting teammate Liam Lawson in the shade.
Turn three proved hazardous - pre-season favourite Russell, Hamilton, and Leclerc all locked up there and slid into the gravel.
Better signs for Aston Martin
With Aston Martin's FP1 all but wiped out by reliability issues, Fernando Alonso and Lance Stroll combined for 31 laps in FP2, posting the 20th and 21st fastest times.
Stroll's fastest lap was six seconds adrift of Piastri's, but it was a better session for the team after Alonso missed FP1 entirely and Stroll managed only three laps.
Both drivers are on limited laps due to the risk of permanent nerve damage from vibration in the car, and the team's race weekend is on a knife-edge due to battery failures.
New team Cadillac had an underwhelming start to Formula 1, with veteran driver Sergio Perez 20th quickest in FP1 and missing most of FP2 due to a sensor issue.
When the Mexican emerged late in the second session, he was unable to post a lap.
His Finnish teammate Valtteri Bottas was also slow, falling to 19th in FP2 from 17th in FP1.
The teams have a final practice session on Saturday before qualifying starts.
Questions remain over how F1's new engine regime will stand up in race conditions.
Early signs are that the cars are slower, with Piastri's best lap in FP2 more than three seconds shy of Leclerc's corresponding time (1:16.439) at Albert Park last year.