The Brazilian, with a time of one minute 35.043 seconds, was almost three-tenths of a second quicker than double world champion Fernando Alonso's McLaren.
Massa's Ferrari team mate Kimi Raikkonen, who won the season-opening race in Australia, will start third on the grid at the Sepang circuit on Sunday alongside McLaren's rookie Lewis Hamilton.
"I think at the end of the day the McLarens were really competitive and it makes us work even harder to have a good race tomorrow," Massa told a news conference.
In a scintillating final lap of qualifying, with the threat of rain, both Raikkonen and Alonso briefly held pole before Massa snatched it from them.
Qualifying results from Sepang:
1. Felipe Massa (Brazil) Ferrari 1:35.043
2. Fernando Alonso (Spain) McLaren 1:35.310
3. Kimi Raikkonen (Finland) Ferrari 1:35.479
4. Lewis Hamilton (Britain) McLaren 1:36.045
5. Nick Heidfeld (Germany) BMW Sauber 1:36.543
6. Nico Rosberg (Germany) Williams - Toyota 1:36.829
7. Robert Kubica (Poland) BMW Sauber 1:36.896
8. Jarno Trulli (Italy) Toyota 1:36.902
9. Ralf Schumacher (Germany) Toyota 1:37.078
10. Mark Webber (Australia) RedBull - Renault 1:37.345
11. Heikki Kovalainen (Finland) Renault 1:35.630
12. Giancarlo Fisichella (Italy) Renault 1:35.706
13. David Coulthard (Britain) RedBull - Renault 1:35.766
14. Takuma Sato (Japan) Super Aguri - Honda 1:35.945
15. Jenson Button (Britain) Honda 1:36.088
16. Vitantonio Liuzzi (Italy) Toro Rosso - Ferrari 1:36.145
17. Scott Speed (U.S.) Toro Rosso - Ferrari 1:36.578
18. Anthony Davidson (Britain) Super Aguri - Honda 1:36.816
19. Rubens Barrichello (Brazil) Honda 1:36.827
20. Alexander Wurz (Austria) Williams - Toyota 1:37.326
21. Christijan Albers (Netherlands) Spyker - Ferrari 1:38.279
22. Adrian Sutil (Germany) Spyker - Ferrari 1:38.415
