Hot Hamilton leads Mercedes one-two in China
Mercedes driver Lewis Hamilton of Britain celebrates on the podium after winning the Formula One Chinese Grand Prix in Shanghai on April 20, 2014 - by Mark Ralston
The British former world champion got away smoothly from pole position and finished 19 seconds ahead of Rosberg, with Ferrari's Fernando Alonso third in front of the two Red Bulls.
Despite winning three races in a row for the first time in his career, Hamilton still trails Rosberg by four points in the title race as he seeks his second world championship.
Red Bull's Daniel Ricciardo held off his team-mate and reigning world champion Sebastian Vettel for fourth spot with the Force India of Nico Hulkenberg coming home in sixth.
"I can't believe how amazing the car is. I was able to look after the tyres and then I was racing myself," said Hamilton on the podium after the race.
"I'm really happy Nico's up here with us. It's great points for the team."
In dry conditions, Hamilton got away cleanly from pole position at the start and by lap six he already had a four-second cushion on the field.
Behind him Vettel moved up from third past his team-mate Ricciardo, as did Alonso who got a flying start in the Ferrari.
The early drama came behind as Felipe Massa in the Williams dived past Nico Rosberg's Mercedes and banged his left rear wheel against Alonso's car.
Rosberg, seemingly mesmerised by Massa's overtaking manoeuvre, then touched wheels with the other Williams of Valtteri Bottas on his outside but came through unscathed.
It took Rosberg two laps to get back past Massa and when the first round of pit stops began on lap 12, the Williams crew could not remove Massa's damaged rear left.
By the time they finally replaced it, Massa had been relegated to last place and the Brazilian eventually finished way down in 15th.
Alonso stopped a lap earlier than Vettel in what proved a masterstroke as, with his rubber up to race temperature sooner, he got past the four-time world champion.
Ricciardo pitted after 15 laps, dropping him behind Rosberg.
Rosberg and Vettel became engaged in a wheel-to-wheel battle for third place on lap 23 from which the Mercedes driver emerged in front.
Their fight enable Ricciardo to close on his team-mate and Vettel was asked to move over, as he had in Bahrain, to let the quicker Ricciardo through.
But Vettel this time was having none of it. "Tough luck," he said of Ricciardo's position over team radio, and he defended his fourth place only to be passed a couple of laps later.
By lap 33 of the 56 Rosberg had Alonso in his sights and was told to "push hard" to catch the Spaniard over team radio.
Alonso responded by pitting, leaving the familiar sight of two Mercedes at the head of the field for the third race in a row until Rosberg himself stopped for a second time.
Vettel was having a frustrating afternoon and with badly grained tyres suffered the ignominy of at one point being passed by the Caterham of Kamui Kobayashi, much to the Red Bull driver's disgust.
Hamilton made his second and final stop on lap 38 and emerged from the pit lane with a 13-second cushion over Alonso.
Rosberg was flying, however, and after setting the fastest lap he re-took second place by easily passing Alonso on a straight.
With four races out of 19 gone, Mercedes already have a stranglehold on the constructors' standings with 154 points, 97 more than second-placed Red Bull.