Positive and negative results for Mercedes at Sochi.
Rosberg, who will be bidding for his seventh win on the trot tomorrow, lapped in 1m35.417s.
He was 0.842s clear of Sebastian Vettel, who won't start from the front row due to his grid penalty for a gearbox change.
Hamilton failed to take part in Q3 as he suffered an apparent MGU-H failure at the end of Q2 having rejoined for an extra run at the end of the session but come straight back into the pits.
"I lost the power, the same like I lost in China," he rued.
Another small cloud hangs over him too, as he's required to visit the stewards due to not following the required etiquette in the Turn 2 run-off after missing the apex.
Story of the session
With Hamilton not taking part in Q3, the door was wide open for Rosberg to cruise and collect his 24th career pole position. He locked up and was forced to abort his seemingly quicker second run after running wide, but in truth he didn't need to improve anyway.
Vettel qualified second but will drop to seventh, so Williams's Valtteri Bottas will start from alongside Rosberg on the front row, ahead of Ferrari's Kimi Raikkonen – who was a tenth slower than his fellow Finn.
Felipe Massa will start fourth for Williams, ahead of Daniel Ricciardo's Red Bull and Sergio Perez's Force India.
Behind the penalised Vettel, Daniil Kvyat will start eighth in the second Red Bull, ahead of Max Verstappen and Hamilton – unless the latter is forced to change engine components which will mean a grid penalty.
Kvyat makes Q3 at Sainz's expense
The big Q2 story was Kvyat's last-gasp lap that just grabbed a place in Q3, pushing out Carlos Sainz Jr's Toro Rosso by three hundredths of a second.
Sainz, who missed qualifying last year after his big practice crash at Turn 13, was joined on the sidelines by Jenson Button's McLaren, Nico Hulkenberg's Force India, Fernando Alonso's McLaren and the Haas duo of Romain Grosjean and Esteban Gutierrez.
"Something happening on the car," complained Grosjean of his lack of grip.
The other action of the session was Ricciardo's right-hand side mirror becoming detached on his final flying lap, but he managed to squeeze through into Q3 in ninth.
Last year's poleman Rosberg set the pace in Q2 with 1m35.337s, almost half a second clear of Hamilton.
Usual suspects exit in Q1
The six drivers who fell at the first hurdle were the closely-matched Renault duo Kevin Magnussen and Jolyon Palmer, Sauber's Felipe Nasr – who had a big lockup and overshot Turn 13 – the Manors of Pascal Wehrlein and Rio Haryanto, and the second Sauber of Marcus Ericsson.
Despite his exit, Palmer reported he was upbeat after the team "solved an issue that's been hurting me for the last couple of grands prix."
Hamilton topped this session on 1m36.006s from Rosberg, but angered the stewards by not following their instructions by staying left of a bollard at Turn 2 after he ran wide.
|6||Daniel Ricciardo||Red Bull Racing||1:38.091||1:37.569||1:37.125|
|7||Sergio Perez||Force India||1:38.006||1:37.282||1:37.212|
|8||Daniil Kvyat||Red Bull Racing||1:38.265||1:37.606||1:37.459|
|9||Max Verstappen||Toro Rosso||1:38.123||1:37.510||1:37.583|
|11||Carlos Sainz Jr.||Toro Rosso||1:37.784||1:37.652|
|13||Nico Hulkenberg||Force India||1:38.562||1:37.771|
|15||Romain Grosjean||Haas F1 Team||1:38.383||1:38.055|
|16||Esteban Gutierrez||Haas F1 Team||1:38.678||1:38.115|
|17||Kevin Magnussen||Renault F1 Team||1:38.914|
|18||Jolyon Palmer||Renault F1 Team||1:39.009|
|20||Pascal Wehrlein||Manor Racing||1:39.399|
|21||Rio Haryanto||Manor Racing||1:39.463|