Hamilton made sure there would be no repeat of Ferrari's surprising win two weeks ago at the Malaysian Grand Prix, conserving his tires to withstand a challenge by the Italian team's Sebastian Vettel and easily capture his fourth Chinese Grand Prix and the 35th win of his career.
Rosberg finished second again and angrily accused his teammate of holding him back in the race.
Hamilton's tire-conservation strategy ensured he could open up a sizeable lead over Vettel after the second pit stop, but Rosberg said at a tense news conference afterward that Hamilton's measured pace allowed the Ferrari driver to stay close to him and caused his tires to wear by the end of the race.
"It's just now interesting to hear from you, Lewis, that you were just thinking about yourself with the pace in front and unnecessarily that was compromising my race," he said. "It was unnecessarily close with Sebastian as a result and it cost me a lot of race time."
Hamilton responded by smiling and saying he didn't intentionally try to impede his teammate.
"It's not my job to look after Nico's race. My job's to manage the car and bring the car home as healthy and as fast as possible and that's what I did," he said. "I just was focusing on myself. If Nico wanted to get by he could have tried, but he didn't."
Tire degradation is what cost Mercedes the race in the tropical heat of Malaysia two weeks ago, so the team was careful not to let it happen again on a warmer-than-expected track in Shanghai.
Hamilton kept his pace in check on soft tires throughout the first half of the race, prompting a frustrated Rosberg to say to his team over the radio, "Lewis is driving very slowly, so tell him to speed up."
The British driver did speed up after Vettel pitted for the second time, clocking his fastest lap time of the day to build a substantial lead by the time he pitted and switched to hard tires a couple laps later.
Vettel faded after the second pitstop and trailed by more than 15 seconds when the safety car came out with two laps remaining after Max Verstappen's Toro Rosso car stalled on the track. The race came to an anticlimactic finish with the drivers rounding the circuit twice behind the safety car.
"We thought it would be a lot closer and we knew the Ferraris were very, very good with their long run pace and also looking after their tires," Hamilton said. "So today the real goal was to manage the tires and my goal was to look after my car."
Hamilton and Rosberg have been friends since childhood, but tensions began to emerge between the teammates as they battled for the drivers' championship last year. They exchanged barbs in the media and even collided on the track during the Belgian Grand Prix, knocking Hamilton out of the race.
Mercedes team boss Toto Wolff said the teammates discussed Sunday's incident after the race without animosity.
"There wasn't any intention from Lewis to slow Nico down in order to make him finish third or worse, 100 per cent," Wolff said.
The safety car may have come out just in time for Vettel, who was holding onto a slight lead over Ferrari teammate Kimi Raikkonen at the end of the race. Vettel finished third and Raikkonen settled for fourth, just missing his first podium finish since the Singapore Grand Prix in 2013.
"We tried everything we could today," Vettel said. "We were really able to put again some pressure on them, especially in the beginning of the race. Toward the end I think they were just too quick."
The Williams cars of Felipe Massa and Valtteri Bottas were fifth and sixth, respectively, followed by Lotus' Romain Grosjean, Sauber's Felipe Nasr, Red Bull's Daniel Ricciardo and Sauber's other driver, Marcus Ericsson.
McLaren achieved its goal of having both cars finish the race for the first time this season — a major step forward as Honda tries to improve the engine on its return to the sport after six years.
Fernando Alonso was 12th and Jenson Button ended up in 14th place after being penalized for a collision with Pastor Maldonado that caused the Lotus driver to retire from the race. Maldonado has yet to finish a race in 2015.
It was another tough outing for Red Bull and Toro Rosso, and their engine provider Renault, as both Daniil Kyvat and Verstappen retired from the race with engine failures. Red Bull's owner has threatened to pull out of F1 if Renault can't make the engine more competitive.