The Australian is competing in his final season in Formula One and still looking for his first win this year. He will look to end Vettel's run of six straight race wins on Sunday.
Webber, who is fifth in the championship, earned his second pole from the past three races and 13th of his career.
"Good day," Webber said, who clocked 1 minute, 39.957 seconds. Vettel timed 1:40.075.
"It was a good lap on a track that, in the past, hasn't been super invigorating for me in terms of layout but we certainly enjoyed qualifying today.
Vettel, who already has his fourth straight F1 title, took pole in four of the past five races.
"I did what I could today but it wasn't enough. That's why I apologized to the team. I messed up a bit on turn 1, it's a tricky corner," Vettel said. "I think it's a great result for the team, first of all."
Mercedes starts on the second row, with Nico Rosberg ahead of Lewis Hamilton, who spun his car in the closing seconds.
"Nico and Lewis looked very strong, especially in Q2," Vettel said. "We found some extra speed in Q3, so congratulations to Mark.
It proved a disappointing afternoon for Ferrari driver Fernando Alonso, who failed to make Q3 for the first time this season and starts from 11th on the grid.
Mercedes is battling with Ferrari for second place in the constructors' championship behind Red Bull, which has already won the title.
Mercedes leads Ferrari by 313-309, with Lotus back in fourth with 285.
"Third place, best of the rest, which is our target for this weekend," Rosberg said.
But Mercedes will have to assess what happened to Hamilton's car.
"Something gave way on the right-hand side," Hamilton said. "I was going through the chicane and it snapped out. I tried to pull away and it wouldn't move."
Hamilton has won one race this season—clinching victory at the Hungarian GP from pole position in July—but has not managed a podium finish in his past five outings.
"This is a very difficult circuit to overtake on so being at the front means everything," Hamilton said. "Hopefully we can get a good start and maybe still challenge for podium positions.
Lotus driver Kimi Raikkonen qualified in fifth spot but was demoted to the back of the grid after his car failed a post-qualifying floor deflection test.
Lotus successfully argued that floor damage caused by track kerbing led to a similar failure by Lotus driver Romain Grosjean at the Hungarian GP, but this time their explanation was not accepted.
Raikkonen's exclusion elevates Sauber's Nico Hulkenberg to fifth place and moves Ferrari's Felipe Massa up to seventh and teammate Alonso back into the top 10.
It has been a frustrating weekend for 2007 champion Raikkonen, who on Friday made a rare public outburst over unpaid wages and threatened not to race in the final two races of the season.
Meanwhile, Alonso's qualifying form has been so bad that he has not even made the second row since qualifying third for the Bahrain GP in April. Massa, meanwhile, has made the top three only once, qualifying in second spot for the Malaysian GP a month earlier.
Because qualifying and the race itself are held at twilight, when the track is considerably cooler at sunset, only a limited amount of useful data could be gained from early afternoon practice runs, when the daily temperature peaked.
But Ferrari continued to struggle on the twisty circuit, just as it did on Friday, with Fernando Alonso down in 11th and Felipe Massa placing 14th in the final practice run.
The design of the track, with its long, sharp turns and hairpin bends, exposes the lack of traction on the Ferraris, an ongoing problem this season and last. Neither Ferrari driver finished higher than eighth over the three practice runs.