His McLaren team-mate Lando Norris came home third ahead of Mercedes’ George Russell and Hamilton with the Ferraris of Carlos Sainz and Charles Leclerc sixth and seventh.
Alex Albon of Williams was eighth, two-time champion Fernando Alsono of Aston Martin ninth and Pierre Gasly of Alpine 10th.
– Perez in the gravel –
After a sweltering day, the sprint race started in warm conditions under floodlights at the Lusail International Circuit, Piastri making an excellent start to pull clear as team-mate Norris was engaged by a cluster of skirmishes behind him.
Norris dropped from second to sixth while Russell went through to second ahead of the two Ferraris with Verstappen fifth before Liam Lawson ran off-track in a cloud of dust, prompting a Safety Car intervention
On re-start, a fiery Alonso pressurised Norris in a wheel-to-wheel battle while Piastri ran wide and allowed Russell through to lead. Logan Sargeant then spun off in his Williams to bring another Safety Car interval.
Piastri had chosen medium compound tyres while Russell, Sainz and Leclerc were all on softs, giving them an early advantage in grip.
Verstappen, in fifth as the Safety Car led into lap six of the 19-lap race, was comfortable in the knowledge that he was on course to clinch his third title by finishing in the top six.
As lap seven began and the Saftey Car went in, Russell stormed into a 1.4 seconds lead ahead of Piastri, who was fending off attacks from Sainz, hoping that his medium tyres would prove more durable in the closing stages.
Perez and Verstappen then began to show Red Bull’s speed, the Mexican moving up to 10th by passing Pierre Gasly and the Dutchman sweeping past both Ferraris in succession on the straight to take third.
On lap 10, Piastri regained the lead, blasting past Russell on the straight while Norris overtook Leclerc for fifth as Perez was entangled in a collision with Esteban Ocon and Nico Hulkenberg, the Mexican spinning across the gravel and out of the race.
Perez was unable to score points and effectively ended his last mathematical hopes for the title, as another Safety Car intervention began, Verstappen being assured of his third crown.
As the racing re-started, on lap 16, it was clear the Dutchman had no intention of taking a third title without a win as he passed Russell down the inside of Turn One to take second and begin his pursuit of Piastri.