With Vettel carrying a five-place grid penalty due to an unscheduled gearbox change, the German will start seventh behind - in qualifying order - Williams’ Valtteri Bottas, Ferrari’s Kimi Raikkonen, Williams' Felipe Massa, Red Bull’s Daniel Ricciardo, and Force India’s Sergio Perez.
Red Bull’s Daniil Kvyat, Toro Rosso’s Max Verstappen and the luckless Hamilton completed the top ten.
Hamilton was downbeat but philosophical after his technical problems, a recurrence of the same issue his car suffered last time out in China. They mean he now faces the possibility of again starting from the back of the grid.
“There’s nothing I can do… I never give up,” said the world champion, who also has to visit the stewards to explain why he did not rejoin the track in the manner required by the race director after running slightly wide at Turn 2 during Q1.
The opening phase saw Hamilton edge out Rosberg with 1m 36.006s to 1m 36.119s - both comfortably faster than they had been in FP3. Vettel was close, but not close enough, with 1m 36.555s.
As Esteban Gutierrez joined Haas team mate Romain Grosjean in progressing to Q2, Kevin Magnussen narrowly beat Renault team mate Jolyon Palmer but both failed to get through. Behind them, Felipe Nasr took 19th for Sauber, as Pascal Wehrlein just headed Manor partner Rio Haryanto. Marcus Ericsson brought up the rear in the second Sauber.
Rosberg owned Q2 with a lap of 1m 35.337s, half a second up on Hamilton and a whole 1.3s up on Vettel.
Further back, Daniil Kvyat delighted the crowd when his final effort lifted him to 10th, and Q3, in the dying seconds. That bumped Toro Rosso’s Carlos Sainz by 0.046s. There was no joy for McLaren either; Jenson Button was left 12th, two places ahead of team mate Fernando Alonso. They sandwiched Nico Hulkenberg’s Force India, as the two Haas cars of Grosjean and Gutierrez finished 15th and 16th.
As Hamilton’s latest ERS drama unfolded and precluded him from running, Rosberg owned Q3 too. His first run yielded 1m 35.417s to Vettel’s 1m 36.259s and Raikkonen’s 1m 36.695s.
Rosberg’s next try saw him faster in the first two sectors before the lap was ruined by an off in Turn 13, but by then the job was long done.
Vettel improved from 1m 36.259s to 1m 36.123s, but drops to seventh after his penalty, which means that with the third fastest time of 1m 36.536s Bottas will make Williams’ first front-row start since Germany two years ago.
Thus, subject to potential penalties for Hamilton, the provisional grid will read: Rosberg, Bottas; Raikkonen, Massa; Ricciardo, Perez; Vettel, Kvyat; Verstappen, Hamilton; Sainz, Button; Hulkenberg, Alonso; Grosjean, Gutierrez; Magnussen, Palmer; Nasr, Wehrlein; Haryanto, Ericsson.