Vettel had topped the first two sections of qualifying but Webber stepped up when it mattered with a lap of one minute 37.242 seconds to beat the German by less than a tenth of a second and claim the 11th pole of his career.
Lewis Hamilton was third in the leading McLaren while championship leader Fernando Alonso, holding just a four-point lead over Vettel, was fourth for Ferrari, but Jenson Button failed to make Q3 and was 11th.
While Vettel will be frustrated at missing out to his team-mate, his chances of taking over the championship lead from Alonso look good with Red Bull proving to be the car to beat so far this weekend.
Hamilton, 42 points adrift of Alonso, recovered well after a disappointing Friday as he tries to keep his title aspirations alive, but he was very fortunate to avoid a collision with Michael Schumacher in the pitlane during Q3.
The German pulled out of his pitbox into the path of the Briton, whose sharp reactions prevented a coming together.
Alonso was fourth and will hope Ferrari's encouraging race pace in practice will yield a strong race result, although he will have one set of super-soft tyres less than his rivals after being forced to use a set to get through Q1, which he ended 16th, just ahead of Hamilton.
Kimi Raikkonen was fifth in the first of the Lotus cars, with Felipe Massa sixth in the second Ferrari.
Romain Grosjean was seventh with Nico Hulkenberg a fine eighth for Force India ahead of the Mercedes of Nico Rosberg and Schumacher.
But it was a disappointing session for Button. The 2009 world champion was trying to improve during the final seconds of Q2 when the Toro Rosso of Daniel Ricciardo stopped in sector three, bringing out the yellow flags.
Button appeared to lift to allow for the caution flags, but others, including Rosberg, improved their times while the yellows were out, dumping the McLaren man out, although the stewards may yet decide to take a look at the incident.
Sergio Perez and Kamui Kobayashi were 12th and 13th for Sauber while Paul Di Resta was another frustrated by the yellows as he ended up 14th.
Pastor Maldonado was 15th ahead of the two Toro Rossos of Ricciardo and Jean-Eric Vergne.
Bruno Senna was again the man to join the Caterhams, Marussias and HRTs in the drop zone in Q1.
The Williams driver could potentially have put Hamilton out as he went for a lap on the super-softs, but a mistake at the penultimate corner ended his chances.
After taking his second pole of the year, and the 200th for a Renault engine, Webber said: "It was a nice qualifying, it was very tight and I was very happy to get the job done today [Saturday] and get the pole position.
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"It was a reasonable lap and we did it when it counted and that is what qualifying is about.
"It's been a tricky last few weeks for me so I am very happy to start from pole and tomorrow [Sunday] is the main day and we are in a good position to do a good job."
Vettel was satisfied with second place, but admitted he had been delayed slightly by Massa's Ferrari ahead of his final lap.
He said: "Overall we can be very happy with the result, we were quite quick in the first session and the second session, and we had a good start to Q3.
"But on the last run, I don't want to blame it on Felipe. I thought he was coming in, but then in the last sector he was right in front of me, so I had to back off which is not ideal when you are just starting a timed lap.
"Nevertheless the second lap was not quick enough, we lost a bit in the middle sector but I think second is a very good position to start from."
Hamilton said: "It's going to be very tough to get ahead of them (Red Bull]. These guys have clearly made quite a big step within the last few races.
"We've got to keep pushing, we're not far off. The race pace for Jenson looked good yesterday [Friday].
"I'm happy that I got a clear lap and was able to put the car as high up as possible."