Charles Leclerc won a close battle with Red Bull's Max Verstappen before taking a classy victory.
After their first pit stops, Leclerc and Verstappen swapped places five times in two laps before Leclerc moved ahead.
The closing laps were packed with drama, with a safety car period and then reliability problems forcing Verstappen's retirement.
Lewis Hamilton took the final podium place for Mercedes after the second Red Bull ofSergio Perez suffered an engine failure at the first corner of the final lap.
Hamilton had looked set for fifth place as Mercedes pace problems became ever clearer during the race but Red Bull's nightmare provided the seven-time champion an unexpected boost.
The irony that Hamilton gained from Red Bull's misfortune in the first race after he lost the world title in the controversial climax to last season will be lost on few.
Leclerc's victory was out of the top drawer and showed his quality as one of the leading lights of the new generation.
If Ferrari can stay competitive, he will be a serious contender for the title.
Verstappen should have taken second place, but Red Bull collapsed in the final three laps.
The Dutchman tried his best, fighting vigorously with Leclerc after their first pit stops, but ultimately losing out in the fight, and was looking set for a frustrated second place before his race unfolded.
He asked what was happening with the battery after a lap into the final sprint, after complaining about heavy steering. He pulled into the pits with three laps to go.
Perez held off Hamilton for third place.
The Mexican spun at the start of the final lap as the engine suddenly stopped and Red Bull went from second and fourth to nothing in a few moments.
After snatching pole position from Verstappen with the very final lap of qualification, Leclerc held off the Dutchman at the first corner and consolidated his lead through the first stint.
The Monegasque was in front by the time Verstappen made his first pit stop, but when Leclerc stopped the next time around, the Red Bull was in front.
The defining period of the race began.
Verstappen dove into the lead into Turn One at the start of the 17th lap after chasing Leclerc for a lap.
Leclerc cut across Verstappen as he was edging ahead, but remained under threat.
After Verstappen passed him at Turn One, Leclerc took the lead at Turn Four, diving to the inside.
Verstappen tried to get into Turn One for a third time, but locked his front tire and slid straight on, allowing Leclerc to take the lead.
The driver from Ferrari built a lead of close to five seconds.
The driver of the car had too much speed for Verstappen.
With just over 10 laps to go, Red Bull threw the dice and fitted soft tyres to Verstappen and Perez's cars for a final sprint to the flag.
The new dynamic had no time to play out as Pierre Gasly pulled off with his Alpha Tauri in flames and the safety car was deployed.
While Verstappen tried to harry Leclerc before he bolted from the last corner, he came under pressure from Sainz.
He held him off for his race to end.
George Russell took fourth for Mercedes ahead of the revived Haas of Kevin Magnussen and Valtteri Bottas, a strong drive from the Finn after a dreadful start dropped him right down the field from his sixth place on the grid.
The new rules introduced this year with the aim of closing up the field and making overtaking easier have shuffled the pack, with Mercedes and McLaren the biggest winners.
The race didn't provide enough evidence to conclude if their intentions have succeeded.
More to come.