The Briton’s victory, following a major upgrade to the McLaren car for this fourth race weekend of the season, was quite the statement after a tricky start to the season for the world champions.
Norris managed the race carefully, ensuring he did not overwork his medium tyres in the opening laps, before extending the gap over Piastri to take control.
Piastri ran close to Norris in the opening laps as Leclerc initially held off a train including the Mercedes drivers, Hamilton and Verstappen.
But Leclerc moved clear of that fight and began to pressure Piastri, until the Australian reasserted his authority to edge away again in the final two laps.
Antonelli made his fifth consecutive poor start in all races this season and was challenged by Russell as they went around the first corner side by side, with the Briton on the inside.
Antonelli fought off that challenge, but Russell overtook him on lap seven at the first corner. A lap later, the Italian dived back into fourth place at Turn 11, at the end of the long back straight, and held the place to the end. His penalty reduced his lead over Russell in the championship to seven points.
The 19-year-old said: “I didn’t even drive well, I made a lot of mistakes, I got track limits, which is something I need to avoid.”
Russell said: “I’m two places forward but not much happier. The improvements from Ferrari, McLaren and Red Bull are daunting.”
Behind the Mercedes, Verstappen barged Hamilton aside at Turn Three on the first lap, the two touching wheels, before the seven-time champion reclaimed the place when the Red Bull’s battery did not deploy out of the final corner of the opening lap.
The pair ran close together until Verstappen passed Hamilton on lap seven. But the move ended with both cars off the track, and Verstappen was advised to hand the place back to his 2021 title rival.
Two laps later, though, Verstappen was through for good, out-braking the Ferrari into the final corner.
Alpine’s Pierre Gasly took the final point for eighth place, ahead of Red Bull’s Isack Hadjar and Gasly’s team-mate Franco Colapinto.
Gabriel Bortoleto finished 11th on the track but was later disqualified because the engine intake air pressure on his Audi exceeded the maximum permitted limit.
Qualifying for Sunday’s main grand prix takes place at 21:00 BST.