Starting second on the grid behind polesitter Hamilton, the German made much the better getaway and proceeded to ease his way clear.
Hamilton came back during the closing laps after Rosberg complained that his tyres were going off – the gap at the chequered flag was 2s – but the Briton also picked up a five-second penalty for crossing the pitlane exit after stopping for tyres.
Rosberg was therefore able to claim his second win of the season and closes back to within 10 points of his Mercedes team-mate in the battle for the drivers’ title.
Felipe Massa finished third for Williams but the Brazilian had to fend off the attentions of Sebastian Vettel in the closing laps. Vettel had run third in the early stages but lost the place after a slow tyre stop from Ferrari.
Valtteri Bottas’s Williams finished fifth with Nico Hulkenberg (Force India), Pastor Maldonado (Lotus), Max Verstappen (Toro Rosso), Sergio Perez (Force India) and Daniel Ricciardo (Red Bull) completing the top ten.
The first five laps of the race were run behind the Safety Car after a heavy collision between Fernando Alonso and Kimi Raikkonen. McLaren’s Fernando Alonso and the Ferrari of Kimi Raikkonen crash on the opening lap of the Austrian GP, leaving one car on top of the other.
Exiting Turn Two on the opening lap, Raikkonen lost control of his Ferrari, which then tangled with Alonso’s McLaren-Honda behind. They then careered into the barriers, with Alonso’s car ending up on top of the Finn’s and leaning against the guardrail.
Credit: Sky Sports