“I found the go-faster button,” Button joked over the radio as his best run on the supersoft Pirelli tyres put him 1.3s down on Rosberg, but ahead of the fourth-placed Toro Rosso of Max Verstappen and the leading Ferrari of Kimi Raikkonen.
There was trouble for Sebastian Vettel in the second Ferrari, which he parked at Turn 8 late on in the session, telling his crew: “Something is not right. I lost drive.” It turned out that the rear left wheel was loose.
Vettel ultimately finished sixth, just ahead of the Red Bulls of Daniil Kvyat and Daniel Ricciardo, split by Valtteri Bottas in the Williams, whose team mate Felipe Massa completed the top ten.
On the soft Pirellis leader Rosberg had lapped in 1m 32.173s, faster than he went in FP1, as Hamilton chased on 1m 32.383s. On the supersofts, Rosberg then did 1m 31.001s, Hamilton 1m 31.242s after edging slightly ahead mid-lap with the fastest sector two time before losing pace in the third.
On the softs, Vettel had got close to them, with 1m 32.650s, but on the supersofts his best was only 1m 33.173s as he made a mistake at the final corner. With 15 minutes to go his session was over.
Others to make an impression were rookie Stoffel Vandoorne who, after losing a chunk of time to Button in the first sector on his soft-tyre run, then matched his McLaren team mate in the next two to go 11th on 1m 32.999s, just seven-tenths down, as he became more confident in his MP4-31.
Pascal Wehrlein again looked good for Manor, pushing ahead of both Saubers and team mate Rio Haryanto to take 19th.
The Haas team were again fast - but fragile. Esteban Gutierrez was 12th, Romain Grosjean 14th, but the Frenchman’s car lost its front wing over the Turn 13 kerbing, prompting a brief Virtual Safety Car period as debris was cleared.