The action was all behind the two leaders, as Piastri from fifth on the grid and Leclerc from ninth sought to make up ground.
Both did so by running long to their pit stops.
Piastri, who was fifth behind Hamilton and Russell in the opening laps, stopped after them on lap 38 and came back to pass both around the outside of Turn Seven, Hamilton on lap 40 and Russell five laps later.
His podium finish extended McLaren’s lead over Red Bull in the constructors’ championship to 42 points.
Hamilton then suffered the same fate at the hands of Leclerc, who stopped on lap 36 and passed him on lap 49.
The Briton had started on the soft tyre, hoping he might be able to jump Verstappen at the start. But the Dutchman held him off as Hamilton attacked at the first corner, and the Red Bull soon began to pull away.
Hamilton made an early stop to change his soft tyres for hards on lap 17, and feared he might not make it to the end of the race. He did, but his aged tyres meant he could do nothing to hold back Piastri and Leclerc.
Russell, starting on the medium tyres like all the other drivers in the top 10 bar Hamilton, ran to lap 27 before stopping.
His tyres were nine laps older than Leclerc’s when the Ferrari caught him, but the better traction of the Mercedes saved him, and Leclerc could not get close enough to pass.
Ricciardo’s fastest lap not only helped out Verstappen in the championship, but may have been a last hurrah for the popular eight-time winner.
There is speculation that Ricciardo might be dropped in favour of Red Bull reserve driver Liam Lawson before the next race, the United States Grand Prix, in Austin, Texas, from 18-20 October.