The Australian led a McLaren one-two ahead of Lando Norris in a race that threatened to unravel the team.
Piastri jumped well from the start and seized the race lead at the opening corner.
He then controlled the race until the team pitted Norris first at the second round of stops, a move designed to protect him from Lewis Hamilton.
It left him ahead of Piastri in the closing stages, and seemingly unwilling to hand the position back.
He eventually, and reluctantly did, as Piastri became the fifth Australian to win a world championship grand prix.
“This is really the day I dreamed of as a kid, standing on the top step of an F1 podium,” the Melburnian beamed.
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“Obviously a bit complicated at the end, but I put myself in the right position at the start.
“Thank you for the team for an amazing effort, an amazing car – hell of a lot of fun racing with McLaren.
“Can’t thank them enough for giving me the opportunity to be in F1, and now to win together 16-18 months, it’s an incredible feeling.”
It was a near-perfect race for the 23-year-old, the only blemish a dropped wheel following his second stop and an off-track moment at Turn 11 that cost him just under two seconds earlier on.
“It’s a beast at the moment,” Piastri said of his car, which was clearly the fastest in Sunday’s race.
“It’s fast in every condition. Today, we had it under control completely.
“An amazing feeling to just be able to manage the race like that, with both cars, and secure a one-two.”
It was a nervy finale with Norris unwilling to hand the lead back to his team-mate.
Given the preferential strategy in lieu of his exposure to Hamilton at the final round of stops, he undercut Piastri as a consequence.
Asked to hand the position back, he did so only in the closing laps after initially extending his advantage.
“The longer you leave it, of course the more you get a bit nervous,” Piastri said of his thoughts in the car.
“It was well executed by the team, and I think it was the right thing.
“I put myself in the right position at the start.
“With the different strategy we had, yes, my pace probably wasn’t as quick as I would have liked in the last stint but I was still in the right position to make it happen.”
The seventh different winner of the season, Piastri remains fifth in the drivers’ championship, now just five points back from Carlos Sainz.
McLaren meanwhile has moved to second in the constructors’ standings, 51 points back from Red Bull Racing.
Piastri also joins an exclusive club of Australian F1 winners, becoming just the fifth member after Jack Brabham, Alan Jones, Mark Webber, and Daniel Ricciardo.
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