His Mercedes team mate Lewis Hamilton, the world championship leader, finished third from the back row of the grid, behind Red Bull's Daniel Ricciardo.
Rosberg started on pole and kept the lead after his main rivals, fellow front-row starter Max Verstappen and the Ferrari pair of Kimi Raikkonen and Sebastian Vettel, collided at the first corner.
That allowed Rosberg to run away at the front and he crossed the line 14.1 seconds ahead of Ricciardo.
The race was briefly halted with nine of the 44 laps completed after a massive crash for Kevin Magnussen, who lost control of his Renault as he crested the fearsome Eau Rouge.
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The Dane, who was taken to hospital for routine checks after suffering a cut to his left ankle, slammed violently into the barriers, prompting officials to first deploy the safety car and then the red flag as marshals worked to repair the damage.
“In general, yes, I had everything under control,” Rosberg told reporters.
“I just had an awesome car and Lewis wasn’t there to battle it out, which made it a less difficult weekend.”
Sunday’s win was the 20th of the Rosberg’s career and sixth of the season.
But it was the 31-year-old’s first since June’s European Grand Prix, reigniting his title challenge after a run of lacklustre races in which he steadily lost ground to Hamilton.
The Briton, winner of six of the last seven races leading up to the Belgian round, still leads the championship but by a narrower nine-point margin with eight of a record 21 races still to run. The triple champion, who had gone into the weekend gunning to become only the third ever driver to score 50 career wins, was happy to come away with a podium finish.
“I honestly didn’t know what was going to happen in the race,” said Hamilton, whose rise up the order was helped by the opening lap collisions and race disruptions.
“I really can’t believe we came so far up to be honest.”
Nico Hulkenberg, who ran as high as second at one stage, finished fourth for Force India.
Team mate Sergio Perez was fifth, on a strong day for the Silverstone-based team that took them ahead of Williams into fourth in the constructors’ standings.
Vettel fought back to finish sixth ahead of Fernando Alonso who also enjoyed a strong race having started dead last.
Ferrari’s Kimi Raikkonen, who had fallen one lap behind the leaders after the opening lap tangle, was ninth with Red Bull's Verstappen finishing a disappointing 11th.
(Editing by Ed Osmond)
