Ferrari's Fernando Alonso, who finished fourth, looked a real threat before fading.
McLaren's Lewis Hamilton, last year's winner at Spa, crashed heavily at Les Combes on the 13th of 44 laps while challenging for fourth place.
Hamilton was unhurt but the incident brought out the safety car while debris was cleared.
Seven times champion Michael Schumacher, the sport's most successful racer, celebrated the 20th anniversary of his Formula One debut at Spa with a fighting fifth place after starting in last position.
Rosberg was sixth, ahead of compatriot Adrian Sutil for Force India and Ferrari's Brazilian Felipe Massa in eighth.
Renault's Russian Vitaly Petrov was ninth and Venezuelan Pastor Maldonado collected his first point in Formula One for Williams in 10th.
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