Piastri departed from pole after topping Saturday's sprint shootout, but having started on mediums the Australian was passed by the soft tyre-shod Mercedes of George Russell on a lap three restart.
But while the softs proved a handy advantage on the restarts, the more robust medium compound was clearly the way to go over the 19-lap contest.
On lap 10 Piastri duly swept past Russell to retake the lead, with only fellow medium runner Max Verstappen a threat in the latter stages.
Afterwards Piastri felt the safety car interruptions were crucial in helping him fend off Verstappen, who had lost positions on a poor first lap but came back to finish second and clinch his third straight world title.
"A very stressful race," Piastri said. "When I saw all the soft guys come through at the start, I thought we were in a bit of trouble and then their tyres fell off pretty quickly.
"The safety cars were my friend today, definitely, once Max got behind me.
"But the pace was reasonable and, in a race where you had to manage a lot the tyres and cars on other compounds, I think we did a really good job, so we're very happy.
"Once [Max] got through into second I thought I was going to be in a bit of trouble, but the pace was good and I managed the tyres well.
"A first sprint win sounds pretty cool."
His team-mate Lando Norris was also shuffled back at the start from second on the grid, but similarly battled his way back into contention as the medium tyres helped him secure a podium, snatching third from Russell on the final lap.
"Oscar has done a mega job, he's had a faultless weekend," Norris added.
"I made a lot of mistakes and he hasn't. He's capitalised and he's done a better job, so just hats off to him. For our team it has been a mega day.
"A tough race for me. A bad start made everything much trickier, but I fought back well, some fun racing, good overtakes, all the way till the last lap on George.
"The softs obviously were a lot better for lap one and the opening stages, but they were lucky there were so many safety cars.
"If there hadn't been so many safety cars, I think easily the medium would have been a better choice."
