Rosberg took advantage of a decisive start in which he surged to the front as Hamilton tangled with the Williams of Valtteri Bottas, damaged his bodywork and slipped down the field.
The German cruised to the chequered flag, sealing maximum points from the first two races of 2016 and a fifth win in succession, ahead of Ferrari’s Kimi Raikkonen and Hamilton, who recovered to take third.
“We still managed to get the car up there and get some points,” said world champion Hamilton, who was also overtaken from pole at the curtain-raising Australian Grand Prix last month.
“Two separate incidents, both equally painful – perhaps today more painful. The team was hoping that potentially there would be a safety car. I had so much damage to the car, I couldn’t fight with Kimi. So, again, damage limitation, congratulations to Nico, an easy race for him I would assume but I’m glad it wasn’t more points.”
Raikkonen’s performance augured well for Ferrari’s competitiveness but his colleague Sebastian Vettel did not even start the race after smoke poured out of his car on the formation lap.
Red Bull’s Daniel Ricciardo was fourth, Romain Grosjean took fifth for new American team Haas and 18-year-old Max Verstappen was sixth for Toro Rosso.
Rosberg’s 16th career win was an eighth consecutive victory for Mercedes and extended his lead over Hamilton in the drivers’ championship to 17 points.
“It’s been an awesome weekend,” he said. “The key was really at the start. I made a great getaway and from then on I was trying to control the pace.”