The Briton topped the session, and the day, with a fastest time of 1m 42.113s - which was just 0.083 seconds faster than Rosberg's 1m 42.196s.
While Rosberg has said he is looking for Williams to push through and separate himself and his title rival Hamilton on Sunday, on today's form it could be a McLaren that gets in on the act after Kevin Magnussen lapped his MP4-29 in 1m 42.895s for third. That closed what had been a 1.7s gap between the Silver Arrows and the chasing pack in FP1, and also suggested that revisions wrought by former Red Bull aerodynamicist Peter Prodromou might already be beginning to have a beneficial effect for the Woking-based team.
The Red Bulls were once again in the top six, with Sebastian Vettel narrowly heading team mate Daniel Ricciardo as they sandwiched Williams' Valtteri Bottas. In the last race of both his reign as world champion and his career with the team, Vettel lapped in 1m 42.959s - compared to Bottas's 1m 43.070s and Ricciardo's 1m 43.183s.
It wasn't a great session for Fernando Alonso whose Ferrari stopped out on the circuit when he was on only his third lap, leaving him marooned in 20th and without a time.
Kimi Raikkonen was seventh for the Italian team, however, with a 1m 43.489s, while Jenson Button took his McLaren to eighth on 1m 43.503s despite a hydraulic problem that kept him in the garage for the first 35 minutes and prevented him from getting a decent run on Pirelli's supersoft tyres.
Daniil Kvyat was ninth in the leading Toro Rosso on 1m 43.546s, ahead of Felipe Massa's Williams on 1m 43.558s and Sergio Perez on 1m 43.746s for Force India.
Pastor Maldonado was Lotus's leader on 1m 44.005s for 11th, splitting Nico Hulkenberg from his Mexican team mate. The German lapped in 1m 44.068s.
Jean-Eric Vergne was 14th for Toro Rosso on 1m 44.157s, while Esteban Gutierrez led Sauber team mate Adrian Sutil with 1m 44.316s to 1m 44.763s. Romain Grosjean was 17th on 1m 44.986s in the second Lotus, but whatever the Frenchman achieves in qualifying tomorrow will be somewhat academic as a 20-place grid drop for changing three elements of his power unit for the sixth time will put him to the back of the grid - or perhaps even the pit lane, depending on how the team decide to proceed after qualifying.
Kamui Kobayashi took 18th for the returning Caterham team, with 1m 45.505s, as new team mate and F1 rookie Will Stevens continued his learning curve in 19th, with 1m 47.057s.