Just 0.084s split the McLaren duo, Piastri having briefly held provisional pole in the dying moments of the qualifying hour.
Norris denied him as McLaren stamped its authority over the field. Max Verstappen was third and almost four-tenths down.
Jack Doohan showed well, easing through Free Practice 1 to qualifying 14th while mistakes proved costly for Liam Lawson on his Red Bull debut, the New Zealander poised for an 18th place start.
It proved a busy start as the pit exit went green to start Qualifying 1, with a traffic jam at pit exit.
After a torrid run through practice, during which he caused to two red flags, Oliver Bearman hit further trouble on his first lap out of the pits.
“It’s broken,” he reported back to the Haas squad.
Also looking to make up for lost time was Liam Lawson.
A power unit issue in final practice saw him stuck in the garage for much of the hour.
He promptly skated long at Turn 3, bouncing over the gravel and using the escape road to rejoin at Turn 4.
That left him among the five drivers in the drop zone ahead of the final runs, together with Pierre Gasly, Nico Hulkenberg, Esteban Ocon, and the luckless Bearman who was stuck in the Haas garage.
A final effort from Lawson looked poised to lift him out of the bottom five before a mistake at the penultimate corner saw him run onto the grass.
He aborted the lap but, with only a minute on the clock, his fate was sealed.
Completing his lap as the chequered flag waved, Gabriel Bortoleto improved to 15th fastest, dropping Mercedes’ Kimi Antonelli into 16th, the first of the five cars eliminated.
He was joined by Hulkenberg, Lawson, Ocon, and the luckless Bearman.
Mercedes promptly revealed it discovered an issue with the bib on Antonelli’s car during his second run, an issue it believes robbed the young Italian of performance and went some way to explain his early elimination.
In the other Mercedes, George Russell topped the segment from Verstappen and Charles Leclerc.
McLaren only showed its hand at the start of Q2, with Piastri going fastest on a 1:15.468s ahead of Norris on a 1:15.556s after their first flying laps.
A spin for Lewis Hamilton exiting Turn 11 saw the Ferrari driver pointing the wrong way seconds before the chequered flag fell on Qualifying 2.
The seven-time champ was still able to progress, his earlier lap good enough to leave him sixth.
Having cleared the first hurdle with ease, Doohan could do no better than 14th best and found himself among the five drivers eliminated.
Topping that list was Isack Hadjar for Racing Bulls followed by the Aston Martin duo of Fernando Alonso and Lance Stroll, then Doohan and Bortoleto, who had a wild slide at Turn 4 in his Sauber.
Norris had nosed his way ahead as the flag fell to lead a McLaren one-two at the end of Q2, with Verstappen third best over Russell, Leclerc, and Hamilton.
Both Williams also escaped the cut, with Carlos Sainz an impressive seventh fastest and Alex Albon ninth.
Completing the top 10 were Yuki Tsunoda in eighth and Gasly in 10th.
Norris had a moment exiting the final corner in addition to a track limits strike at Turn 4 that deleted his 1:15.921s.
It was a time that would have left him fourth after the initial runs, but instead, he was 10th without a time to his name.
Verstappen topped the list from Russell, Leclerc, and Piastri, the McLaren driver well off the pace he managed even at the end of Qualifying 2.
The final flurry began with three minutes remaining, the McLaren duo at the head of the train heading out on track.
That surged Piastri onto provisional pole, a position he held for seconds as Norris flashed across the line behind him, 0.09s faster than his team-mate.
Nobody had an answer to the papaya juggernaut with Max Verstappen third ahead of George Russell and the impressive Yuki Tsunoda for Racing Bulls.
Leclerc was the first of the two Ferraris in seventh followed by Hamilton, Gasly, and Sainz rounding out the top 10.
The Formula 1 Australian Grand Prix begins tomorrow at 15:00 AEDT.
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