Piastri pounced on Norris on Lap 5, following Verstappen through at Turn 4 to steal second place away from his McLaren team-mate.
The trio had been engaged in an enthralling tussle, with Norris skating up the inside of Verstappen at Turn 3.
However, he then failed to defend the spot as the Red Bull Racing driver dived back to the inside at the following corner to steal the place back.
With Norris moved aside, Piastri seized the opportunity to follow Verstappen through in an entertaining exchange.
“I obviously had quite a good start compared to Lando, and I then just managed to stay in the DRS and got to the back of him,” Piastri recounted of the early stages, when he sat in wait behind Verstappen and Norris.
“I was sitting there with my popcorn waiting for whatever was going to unfold, obviously just staying patient, and I managed to get Lando. Not quite enough to get Max.”
Piastri finished second in the Sprint, seeing off a challenge from his team-mate in the latter stages who was self critical after the fact.
“I definitely should have done a bit better in my battle,” he admitted.
“I had to make the most of my opportunity, then I messed it up and left the door open like an amateur.”
He was no easier on himself when he fronted the written press later.
“I needed to do a better job, and just did something pretty stupid and silly, which was very smart to me,” he lamented.
In their battle in the second half of the Sprint, Piastri never seemed phased with the Australian never going defensive, or showing any sign of cracking despite the intense pressure he was under.
“Once the car behind gets into DRS, they have three shots at it,” Piastri explained.
“To be honest, the tyres at that point where so hot for everybody that the DRS wasn’t having anywhere near as much of an impact as it did at the start of the race.
“So the last few laps it was a bit more comfortable but all it would take was one mistake.”
Second further underscored the turnaround from the Spanish Grand Prix last weekend.
There, Piastri struggled to match his team-mate with the 23-year-old suggesting the team had understood the reasons at play.
“We’ve got all the answers from Barcelona on what we did wrong and what we wrong in the weekend,” he explained.
“I was much happier with the car in practice straight away, and obviously, in Sprint quali yesterday, it was a good result, and today as well.
“So yeah, oping Barcelona stays as a one off.”