The Briton was 0.449 seconds faster than Rosberg and nearly a second quicker than Red Bull’s Daniel Ricciardo’s in third.
I have not had a Friday like this for a long time
“It’s going really well,” said Hamilton. “It’s been a great day. It feels like a long break and to get back in the car and feel the positive steps made with the car.
“Big thank you to the team because the car’s feeling a lot better this weekend and today has been a smooth day.
“I have not had a Friday like this for a long time.”
Red Bull’s defending champion Sebastian Vettel was forced to sit out the session after an electrical fault to his car during first practice.
“We had a simple failure in one of the looms this morning, which caused a short and meant the car stopped,” said Vettel.
“We had to change the chassis loom, which is a big job so I wasn’t able to go out this afternoon. It’s a small failure, but a big consequence; there was nothing new on that part of the car, it was something new that happened in that area.
“Luckily it happened today (rather than tomorrow), but unfortunately we lost the chance to prepare for Sunday with two cars, so I have to rely on what Daniel did today and get into the rhythm straight away tomorrow.”
1. Lewis Hamilton Britain Mercedes-Mercedes 1m 25.524s
2. Nico Rosberg Germany Mercedes-Mercedes 1m 25.973s
3. Daniel Ricciardo Australia Red Bull-Renault 1m 26.509s
4. Fernando Alonso Spain Ferrari-Ferrari 1m 27.121s
5. Kimi Raikkonen Finland Ferrari-Ferrari 1m 27.296s
6. Kevin Magnussen Denmark McLaren-Mercedes 1m 27.788s
7. Jenson Button Britain McLaren-Mercedes 1m 27.811s
8. Felipe Massa Brazil Williams-Mercedes 1m 27.824s
9. Pastor Maldonado Venezuela Lotus-Renault 1m 27.866s
10. Daniil Kvyat Russia Toro Rosso-Renault 1m 28.049s
11. Nico Hulkenberg Germany Force India-Mercedes 1m 28.074s
12. Jean-Eric Vergne France Toro Rosso-Renault 1m 28.246s
13. Adrian Sutil Germany Sauber-Ferrari 1m 28.284s
14. Valtteri Bottas Finland Williams-Mercedes 1m 28.698s
15. Esteban Gutierrez Mexico Sauber-Ferrari 1m 29.105s
16. Sergio Perez Mexico Force India-Mercedes 1m 29.129s
17. Romain Grosjean France Lotus-Renault 1m 29.493s
18. Jules Bianchi France Marussia-Ferrari 1m 29.991s
19. Max Chilton Briton Marussia-Ferrari 1m 31.148s
20. Kamui Kobayashi Japan Caterham-Renault 1m 31.338s
21. Marcus Ericsson Sweden Caterham-Renault 1m 31.586s
22. Sebastian Vettel Germany Red Bull-Renault no time
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Daniel Sturridge
BIOGRAPHY: Kepa Arrizabalaga