The McLaren driver knocked Lotus driver Romain Grosjean off top spot by just under a tenth of a second during the flurry of soft tyre qualifying simulations in the final minutes of the session.
This suggests that he will be in the mix for pole position, although Sebastian Vettel, who ended the morning an unobtrusive 13th, justified his status as the man to beat by setting the fastest times of all in the first and second sectors before aborting his only flier on softs late on.
After a quiet opening 10 minutes of the session, first Grosjean and then team-mate Kimi Raikkonen topped the timesheets, although it was Red Bull driver Vettel who set the best time of the medium-shod runs, posting a 1m38.434s just after the halfway point of the one-hour session.
During the medium runs, there were few major incidents, although Pedro de la Rosa did spin his HRT after losing it under braking for the final corner.
Grosjean was the first to bolt on the soft tyres after half an hour, jumping to the top of the times.
His lap was good enough for second overall, with Raikkonen, who took advantage of an uncongested circuit to complete his qualifying simulation with 10 minutes to go, proving that Lotus will be strong this afternoon by lapping just a tenth slower.
Force India pairing Nico Hulkenberg and Paul di Resta carried their impressive Friday form over by setting the fourth and fifth fastest times ahead of Sauber driver Sergio Perez.
Several big names were in unfamiliar territory in the bottom half of the timesheets. Fernando Alonso ended up 12th after a big lock up at Turn 12 during his soft tyre run that forced him to take to the run-off area, with Vettel one place behind him with a time set on mediums.
Nico Rosberg was down in 15th, but it was Red Bull driver Mark Webber who endured the worst session. He completed just four laps before a technical problem brought his morning to a close, meaning that he didn't get the chance to run on soft tyres in preparation for qualifying.
FREE PRACTICE SESSION THREE:
1. Jenson Button (Britain) McLaren 1:38.562
2. Romain Grosjean (France) Lotus 1:38.655
3. Kimi Raikkonen (Finland) Lotus 1:38.759
4. Nico Huelkenberg (Germany) Force India 1:38.819
5. Paul Di Resta (Britain) Force India 1:38.892
6. Sergio Perez (Mexico) Sauber 1:39.084
7. Michael Schumacher (Germany) Mercedes 1:39.141
8. Lewis Hamilton (Britain) McLaren 1:39.178
9. Felipe Massa (Brazil) Ferrari 1:39.318
10. Pastor Maldonado (Venezuela) Williams 1:39.357
11. Kamui Kobayashi (Japan) Sauber 1:39.358
12. Fernando Alonso (Spain) Ferrari 1:39.395
13. Sebastian Vettel (Germany) RedBull 1:39.434
14. Bruno Senna (Brazil) Williams 1:39.543
15. Nico Rosberg (Germany) Mercedes 1:39.946
16. Jean-Eric Vergne (France) Toro Rosso 1:40.037
17. Daniel Ricciardo (Australia) Toro Rosso 1:40.134
18. Heikki Kovalainen (Finland) Caterham 1:40.681
19. Mark Webber (Australia) RedBull 1:41.282
20. Vitaly Petrov (Russia) Caterham 1:41.931
21. Pedro de la Rosa (Spain) HRT 1:42.758
22. Charles Pic (France) Marussia 1:42.815
23. Narain Karthikeyan (India) HRT 1:42.943
24. Timo Glock (Germany) Marussia 1:43.124