Rosberg, who also captured his first pole on Saturday, finished 20.6 seconds ahead of McLaren driver Jenson Button.
“It’s an unbelievable feeling,” the 26-year-old German said. “It’s been a long time coming for me, and for the team as well over the past two years and a bit. Now it’s finally here.
“It’s just nice to see how quickly we are now progressing. I didn’t expect to be that fast today.”
Lewis Hamilton of McLaren was third, followed by the Red Bull duo of Mark Webber and Sebastian Vettel in fourth and fifth.
Vettel started 11th on the grid and at one stage moved up to second, but the two-time defending world champion couldn’t hold off Button, Hamilton and Webber in the closing stages.
Rosberg’s teammate, seven-time world champion Michael Schumacher, had also been expecting to perform well after finishing third in qualifying and moving up to the front row after Hamilton, who qualified second, was penalized for a gearbox change. But the German retired on the 13th lap after his right front wheel was improperly fitted during his first pit stop.
For Mercedes, the victory is evidence it has remedied the quick tire degradation problem that led to disappointing results in the first two races of the year. Rosberg and Schumacher have been fast in qualifying this season but failed to keep up with other teams when it mattered in the races.
It was Mercedes’ first victory since it bought out Brawn GP at the end of 2009. Mercedes is also the third different team to win a race this year, following Button’s victory at the Australian GP for McLaren and Fernando Alonso’s win at the Malaysian GP for Ferrari. The 2011 constructor’s champion, Red Bull, is still looking for its first win.
Rosberg drove just one lap in the final session of qualifying to preserve his tires, and said an improved setup helped take the pressure off his tires on Sunday to allow his team’s strategy to pay off.
“Before the race, that was our plan,” he said. “The tires lasted for exactly the amount of laps that we were hoping for, so it all just went to plan.”
Rosberg also benefited from a sloppy pit stop by Button at the end of the 39th lap when he lost several crucial seconds and came out of the pit behind a pack of drivers. As Button jockeyed with Vettel, Webber, Hamilton and Lotus drivers Kimi Raikkonen and Romain Grosjean for position, Rosberg was able to widen his lead to 25 seconds and coast to victory.
“I stopped on the marks (in the pits) and we had a problem with the rear of the car, so I was stuck there for nine or 10 seconds,” Button said. “It was a pity because when I exited the pits I had four cars in front of me, cars that I wouldn’t have been racing, and I would have had a nice clear track to hopefully hunt down Nico.”
The battle for the minor places featured wheel-to-wheel racing with Button and Hamilton eventually coming out on top in the closing laps. The final stages witnessed a spectacular collapse by Raikkonen, who also only pitted twice in the race but was unable to hold his place as his tires slowly gave out. The Finn dropped from second to sixth on the 48th lap and then slipped to 12th on the next lap before eventually finishing 14th.
As Raikkonen fell down the order, Vettel took second and looked to be headed for the podium after a disastrous performance in qualifying left him in 11th position on the starting grid.
But his intermediate tires also started to wear out after a two-pit strategy, allowing the McLarens to catch him. Button slipped by the German on the inside of a hairpin turn in the 51st lap, and Hamilton and Webber followed in the closing laps.
“I had no tires left at the end of the race,” Vettel said.
Schumacher had been hoping for his first podium finish since his comeback in 2010 after posting solid times in practice this week on the Shanghai circuit. Instead, he retired from a race for the second time this season. In Melbourne, he ran wide over the grass at the first turn and was forced to quit soon after with a gear problem.
Mercedes was fined €5,000 ($6,540) after Sunday’s race for the unsafe release from the pits.
“I don’t have any hard feelings,” he said. “I feel a bit sorry for one of my boys that I guess he feels responsible, but it’s part of the game.”
With his third third-place finish of the season, Hamilton took the lead in the driver standings with 45 points, two ahead of Button. Fernando Alonso of Ferrari is third with 37 points, followed by Webber (36) and Vettel (28). Rosberg rise to sixth with 25.
McLaren leads the constructor standings with 88 points, followed by Red Bull with 64 and Ferrari on 37.
