The Australian, who will quit Formula One at the end of the season, will start at the front of the grid for the 13th time in his 12-year career and the second time in three races after qualifying 0.1 seconds quicker than Vettel.
Mercedes fill the second row at the Yas Marina Circuit, with Nico Rosberg qualifying third and Lewis Hamilton fourth despite spinning off on his final lap.
Fernando Alonso, battling to hold on to second place in the drivers' standing, qualified outside of the top 10 for the first time this year, in 11th.
But his chances of clinging on received a real boost when his closest rival, Kimi Raikkonen, who had been due to start fifth, was sent to the back of the grid after his Lotus failed a front-floor deflection test. The Finn, who will move to Ferrari next season, earlier in the week threatened to boycott the race claiming he had "not been paid all year".
Vettel, who is chasing his seventh win in a row after wrapping up a fourth successive title with victory from pole in India last weekend, said he made a mistake in turn one.
"I was pushing hard, that's the reason behind it," he said. "If you push to the maximum you may make mistakes. I'm not very proud of that. But I did what I could and it wasn't enough to be on pole. Mark deserves to be there. It was a great result for the team. I should have done a little bit better, but I don't know if it would have been enough. He did a great job, no mistakes."
Webber said: "The weekend has gone pretty smoothly for us so far. It's not the easiest venue because of the changing temperatures. We run in the afternoon and then at night, so you have to be on top of the changing conditions as a driver and also from an engineering perspective.
"It wasn't the most electric start to Q1 or Q2, but we made changes to the car as the session went on and I got more comfortable. I'm happy with the pole and we're really looking forward to the race."
Ferrari are desperate to overhaul Mercedes in the chase to finish second behind Red Bull in the constructors' championship but had appeared to be struggling in practice.Alonso, whose team-mate Felipe Massa lines up seventh, said: "Qualifying was as difficult as the rest of the weekend, but in some races, starting 11th on new tyres can help, so let's hope that's the case here. It is without a doubt better to make it through to Q3 but unfortunately I didn't manage to get a very clean lap and I didn't manage to make it by a few tenths.
"This is one of the tracks where we suffer a bit more than usual, but in general our Sunday performance is better and so, again this time, our approach to the race is positive. We must absolutely get a good start, stay focused and run a perfect race."
Alonso added: "It is only Saturday. Maybe tomorrow we will finish with both cars in the podium. The important thing is Sunday and to get more points than our competitors and keep fighting for second in the constructors' championship. I'm still confident that on Sunday we will get some good points, more points that our competitors."
Force India's Paul di Resta will start one place behind Alonso in 11th. The Scot, eighth in India last weekend, said: "I'm feeling good in the car, which has worked well all weekend and I'm optimistic we have a good chance of picking up some points.
"The car is responding well and I also think we are more suited to the race than qualifying.
"There's a long race ahead of us, but we will work hard to put together a good strategy tonight and try to push our way forward in the race."
Meanwhile, F1 commercial chief Bernie Ecclestone said yesterday a deal has been done for India to return to the Formula One calendar in 2015 and for six years beyond that if tax problems with the country's authorities can be overcome. The race has been dropped for 2014 with its future uncertain.