Early on there were plenty of cars out on track but the session was red-flagged 15 minutes in because of Sergio Perez's left-rear tyre failure.
There was a lot of debris on track and the marshals had to clear it before the cars could return pacesetting.
The Aussie was replaced at the top of the leaderboard by Lewis Hamilton with 20 minutes of the session left before Hamilton's teammate Rosberg also sneaked ahead of the Red Bull man into second.
It looked as if Hamilton would delight the home crowd before Rosberg went quicker in the final stages.
Third practice full standings:
1. Nico Rosberg (Mercedes)
2. Lewis Hamilton (Mercedes)
3. Sebastian Vettel (Red Bull)
4. Mark Webber (Red Bull)
5. Romain Grosjean (Lotus)
6. Daniel Ricciardo (Toro Rosso)
7. Fernando Alonso (Ferrari)
8. Kimi Raikkonen (Lotus)
9. Adrian Sutil (Force India)
10. Paul Di Resta (Force India)
11. Jean-Eric Vergne (Toro Rosso)
12. Jenson Button (McLaren)
13. Pastor Maldonado (Williams)
14. Nico Hulkenburg (Sauber)
15. Felipe Massa (Ferrari)
16. Valtteri Bottas (Williams)
17. Esteban Gutierrez (Sauber)
18. Sergio Perez (McLaren)
19. Charles Pic (Caterham)
20. Jules Bianchi (Marussia)
21. Max Chilton (Marussia)
22. Giedo van der Garde (Caterham)