Rosberg suffered an engine problem early on and did not record a time until halfway through the session but ended up 0.242 seconds quicker than Hamilton in second.
Daniel Ricciardo underlined the step forward Red Bull have made with their car in recent races by taking third.
The session was interrupted by a crash for Lotus driver Pastor Maldonado.
The Venezuelan lost control at the Malmedy right-hander at the top of the circuit and spun into the barrier on the inside of the track, damaging the front of the car.
The incident justified Lotus’s decision to save their sole example of a new front-wing design they have brought to this race for his team-mate Romain Grosjean, who will not drive until the second session after handing his car to reserve driver Jolyon Palmer for the first.
The Ferraris of Kimi Raikkonen and Sebastian Vettel were fourth and fifth, ahead of the second Red Bull of Daniil Kvyat and the Toro Rosso cars of Max Verstappen and Carlos Sainz Jr.
Force India’s Sergio Perez and Williams’s Valtteri Bottas completed the top 10.
The upgraded Honda engine in the McLarens was a disappointment, with Fernando Alonso setting 16th fastest time and Jenson Button 18th. The Spaniard was 0.723secs clear of the Englishman.
Honda F1 boss Yasuhisa Arai had said he hoped the combustion upgrade to the engine for this race would bring the Japanese company level with the engine performance of Ferrari, regarded as a close second to standard-setters Mercedes.
But the speed trap times showed that, at least in the specification in which it was running on Friday morning, the Honda was still a long way off that.
Alonso was around 15km/h slower than Hamilton’s Mercedes through the speed trap at the end of the long straight after Eau Rouge.
By contrast, he matched the pace of the fastest car, Ricciardo’s Red Bull, at the second speed trap, which is between the Stavelot and Paul Frere corners at the end of the second sector, and is a measure of corner exit speed more than engine power.
Ricciardo’s pace was extremely impressive – the Australian was just 0.049secs slower than Hamilton over the lap on the track where he took his third and most recent F1 victory in this race last year.
Red Bull have made significant progress with their car following an upgrade at the British Grand Prix two races ago and it is now vying with Mercedes for the honour of best chassis in F1.
Red Bull’s Renault engine still lags behind the Mercedes and Ferrari cars on engine performance.
Just 0.4secs separated Rosberg in first place from Raikkonen in fourth, raising hopes of a close, competitive weekend.