Norris finished third in Albert Park, one spot ahead of Piastri in a race that saw Max Verstappen and Lewis Hamilton forced out with mechanical issues.
In the early stages, Norris ran as high a second following Verstappen’s exit but fell behind his Aussie teammate at his first stop on Lap 14.
Piastri had boxed on Lap 9 and climbed up the order as those around him stopped, leaving him third before being moved aside on the run into Turn 3 on Lap 29.
“That swap wasn’t even strategic, that was executional,” explained McLaren team boss Andrea Stella when asked by Speedcafe.
“The swap would have happened naturally because Lando hand much fresher tyres.
“Every one lap you gain on tyres makes your car much, much faster than somebody that stopped before you because the tyres lose almost between half a tenth and a tenth per lap.
“So Lando was always going to overtake Oscar. We called the swap to avoid the discomfort.”
When Norris passed, he did so with tyres that had completed 14 laps rather than the 19-lap old rubber Piastri had fitted and pulled away once released.
The Australian stopped for a second time on Lap 39, a lap before Norris, as they ran with much the same strategy to the end of the race.
“I think once I put that last set of tyres on, they held on a bit better,” Piastri explained post-race.
“Once I grained the tyres in the middle stint, I just couldn’t really get them back.
“Some things to learn and go through and see what I could have done better but I think definitely a step in the right direction.”
Heading into the weekend, Piastri suggested fifth was the best realistic result given the pace of Red Bull Racing and Ferrari ahead.
McLaren proved more competitive than expected, and was able to hold station with Ferrari for much of the race, which in turn appeared closer to Red Bull Racing – for the brief period Verstappen was in the race, at any rate.
That made the podium a possibility on a weekend when it had initially looked out of reach.
“I knew it was a possibility at one point and if I was quick enough in the middle, then it could have been a reality,” Piastri explained of his shot at a top-three finish.
“With the different strategies we had and the tyre difference in terms of stop lap, I was expecting Lando to be quicker at that point.
“I would have loved to have been one spot higher but I think, for the team, it’s been an amazing weekend and honestly, very happy with the gap to Ferrari, especially, being a lot smaller.”
With Norris third and Piastri fourth, McLaren left Australia with 27 points.
By contrast, Mercedes left Melbourne empty-handed after Hamilton retired with engine problems and George Russell crashed out, triggering the Virtual Safety Car under which the race ended.
It leaves McLaren a clear third in the constructors’ championship with 55 points. Red Bull Racing tops the standings with 97 points, four ahead of Ferrari.
Aston Martin now lies fifth on 25, one point behind Mercedes. RB has six points and Haas has four points. After three rounds Piastri is fifth in the drivers’ championship with 28 points, one more than Norris.