Rosberg posted his second career pole and the best performance of the year for the 27-year-old German who has retired early in two of the three races. He was forced by the team to finish behind teammate Lewis Hamilton in fourth place in Malaysia.
"Yes! Come on guys, that's how it's done," Rosberg yelled into the radio.
Rosberg timed 1:32.330 to finish 0.254 in front of Vettel — the three-time defending Formula One champion — and 0.337 ahead of Alonso, who won last week's Chinese Grand Prix.
"As a team, I think we worked really during the night to improve the car because yesterday we were really struggling," Rosberg said. "So that's been going well. I'm really, really happy. That's a fantastic result. That's great for tomorrow."
The race has been criticized by rights groups who have accused the government of trying to gloss over abuses, while anti-government opponents have had almost daily protests over demands for a greater voice in the Gulf country's affairs. Several clashes were reported Saturday, including in the old quarter of the capital Manama and a village close to the circuit where protesters set fires.
Some of those protests on Friday turned violent, with clashes between thousands of stone-throwing youths and riot police firing bird shot and tear gas.
Crown Prince Salman bin Hamad Al Khalifa, touring the paddock, said he was pleased that the protests have been mostly peaceful and called the race a force of good for the country. Asked about the empty stands, he said about 15,000 came to the 45,000-seat circuit Friday and he expected bigger crowds Saturday.
"Keeping Bahrain connected to the international community is a very important thing for us," the crown prince said. "It stops people from looking inwards and allows us to look outwards. It gives people connections to the outside world they otherwise wouldn't have. I think today and this weekend is about sport and transcending conflicts and celebrating what is great about humanity."
Meanwhile on the track, Vettel has struggled much of the season to adjust to the softer tires compounds this year. He said he was "not disappointed" to be starting second. He only has one pole all season.
"Congratulations to Nico. He put a very strong lap in. It was all his today," Vettel said. "When I got told the gap to P1, to Nico, it was clear that even with the perfect lap he was unbeatable today. But nevertheless, very happy."
Fastest in third practice, Alonso had the chance to better Rosberg's time but committed several errors on his final lap. The Spaniard later said the team realized they were about a half-a-tenth or one-tenth slower than their fastest lap after the miscues so "we decided to come in just to save one lap on this tires."
"Very, very happy with third place," Alonso said. "Normally in qualifying, we're struggling a lot but today the car was very competitive in qualifying and this puts us in a strong position to start tomorrow's race with the group of leaders and fight for the podium with a little bit more margin."
Hamilton was fourth but will start ninth following a five-grid penalty for a gear box change. Mark Webber of Red Bull, who was fifth but was given a three-grid penalty last week in China, will start seventh. This will be Webber's 200th grand prix.
The penalty is another headache for Hamilton. He has struggled with the hot and sandy conditions in practice, finishing no higher than 10th in the first two sessions and damaged his rear left tire at the end of the third.
Hamilton has had a successful start in his first season at Mercedes after joining from McLaren. He has finished on the podium in the past two races and took pole position at the Chinese Grand Prix.
The dusty and hot track was not kind to Lotus drivers, with Kimi Raikkonen only ninth fastest and his teammate Romain Grosjean managing 11th.
McLaren also struggled, fulfilling a prediction made by Team Principal Martin Whitmarsh that its car would have trouble with the Bahrain circuit. Jenson Button was 10th fastest while teammate Sergio Perez was 12th.
The crown prince also dismissed allegations by rights groups that the race is used by the Sunni-led government to gloss over problems with its majority Shiite population. The race was cancelled in 2011 due to the Arab Spring-inspired uprising and was overshadowed last year by massive protests outside the circuit — including an
The race last year was overshadowed by the huge anti-government protests and a firebomb that briefly delayed a Force India car and prompted the team to pull out of the second practice.
"We've never used this race to say that everything is fine," the crown prince said. "We recognize there are issues in the country but they are to be solved through a political process, which is well under way. I can name at least four other grand prix venues which have political problems but don't seem to attract that kind of attention."