McLaren's Kevin Magnussen, standing in for the absent Fernando Alonso, and Red Bull's Daniil Kvyat were unable to start after both suffered failures on their formation laps.
The two Manor Marussia cars were scratched on Saturday after failing to participate in qualifying or any practice sessions, while Williams driver Valtteri Bottas was ruled out of the race with a back injury less than an hour before the start.
After a chaotic start that saw Lotus driver Pastor Maldonado crash into the barrier on turn two after being nudged from behind, Hamilton and Rosberg sped away from the chasing pack.
Opening a 15-second gap to third placed Felipe Massa after the 20th lap, Hamilton successfully kept his team mate Rosberg at arm's length.
Following a week of legal battles, Sauber were buoyed by a fifth place finish for Brazilian rookie Felipe Nasr, gaining their first points since 2013.