The session was canceled after only two of the three sections on the grounds that conditions had weakened to the point that the track was excessively unsafe.
Ferrari's Sebastian Vettel took fifth yet will be downgraded 10 places.
Hamilton needs to beat Rosberg by two focuses and Vettel by nine to seal his third title this weekend.
The Red Bulls of Daniel Ricciardo and Daniil Kvyat will be on the second column with the Force India autos making up the third after Vettel's downgrade.
Vettel and fellow team member Kimi Raikkonen, who qualified eighth, have been punished for utilizing more than the allowed number of motors.
Power India's Sergio Perez will begin fifth in front of partner Nico Hulkenberg.
The Ferrari drivers' punishments mean Williams' Felipe Massa, who qualified ninth, will begin seventh, in front of Toro Rosso's Max Verstappen and McLaren's Fernando Alonso.
"I felt OK with the auto," Rosberg said. "It is very testing - the auto snaps abruptly, however I got a decent lap together."
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