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The German celebrated his seventh pole of the season with a time of 1 min 18.773sec, just 0.4 seconds quicker than his Australian team-mate as the Red Bull cars were in a league of their own.
The 23-year-old set off from the front of the grid at last weekend's German Grand Prix only to suffer a poor getaway to finish third, and he said he was hopeful of making up for that on Sunday.
"We found the problem from last week that made the bad start so hopefully we can have a normal start tomorrow," Vettel told the BBC.
"Usually in Hungary it is important to be on the clean side. The start is important but there are 70 laps after that. It will be an exciting race."
Ferrari duo Spaniard Fernando Alonso and Brazilian Felipe Massa, almost a second slower, will start in third and fourth ahead of drivers' championship leader Lewis Hamilton of Mclaren.
Alonso, who won in Hockenheim last Sunday after Ferrari controversially arranged for the Spaniard to overtake his teammate Massa, was impressed with Red Bull's performance.
"We found a big gap between Red Bull and us this weekend, so we maximised our potential today. We did our job which is to be best of the rest. Hopefully tomorrow we can make it a more difficult race for them because so far this weekend it has been too easy."
German Nico Rosberg was sixth quickest for Mercedes followed by Russian Vitaly Petrov who out-qualified his Renault team-mate Robert Kubica for the first time this season.
Spaniard Pedro de la Rosa of Sauber will start in ninth ahead of Williams driver Nico Hulkenberg.
Vettel led the Red Bull assault in the Q1 opening mini-session which saw Japan's Kamui Kobayashi of Sauber eliminated along with the three new teams.
Kobayashi appeared to have been held up by Bruno Senna of Hispania on his final flying lap and was pipped to the 17th fastest time in the final minute of the session by Force India's Adrian Sutil.
That meant he joined Timo Glock of Virgin, Lotus drivers Heikki Kovalainen and Jarno Trulli, Lucas Di Grassi in the second Virgin and Senna ahead of his Hispania team-mate Sakon Yamamoto.
McLaren's worst fears were realised in Q2 when their defending drivers' world champion Jenson Button failed to make the top ten.
Button, who will start in 11th place on Sunday, told the BBC: "In practice I had good balance, but I struggled with the car in qualifying.
"I was OK on the prime tyres, but I couldn't get the options working. It's tough, but we were never going to be on the front two rows here. At least I'm on the clean side of the grid. We can still pick up good points."
He starts ahead of Rubens Barrichello in the second Williams, Sutil, Michael Schumacher in the second Mercedes, Sebastien Buemi of Toro Rosso, Vitantonio Liuzzi in the second Force India, and Jaime Alguersuari in the second Toro Rosso.
Qualifying:
1. Sebastian Vettel (GER/Red Bull-Renault) 1:18.773
2. Mark Webber (AUS/Red Bull-Renault) 1:19.184
3. Fernando Alonso (ESP/Ferrari) 1:19.987
4. Felipe Massa (BRA/Ferrari) 1:20.331
5. Lewis Hamilton (GBR/McLaren-Mercedes) 1:20.499
6. Nico Rosberg (GER/Mercedes) 1:21.082
7. Vitaly Petrov (RUS/Renault) 1:21.229
8. Robert Kubica (POL/Renault) 1:21.328
9. Pedro de la Rosa (ESP/Sauber-Ferrari) 1:21.411
10. Nico Hulkenberg (GER/Williams-Cosworth) 1:21.710
Eliminated in Q2:
11. Jenson Button (GBR/McLaren-Mercedes)
12. Rubens Barrichello (BRA/Williams-Cosworth)
13. Adrian Sutil (GER/Force India-Mercedes)
14. Michael Schumacher (GER/Mercedes)
15. Sebastien Buemi (SUI/Toro Rosso-Ferrari)
16. Vitantonio Liuzzi (ITA/Force India-Mercedes)
17. Jaime Alguersuari (ESP/Toro Rosso-Ferrari)
Eliminated in Q1:
18. Kamui Kobayashi (JPN/Sauber-Ferrari)
19. Timo Glock (GER/Virgin-Cosworth)
20. Heikki Kovalainen (FIN/Lotus-Cosworth)
21. Jarno Trulli (ITA/Lotus-Cosworth)
22. Lucas Di Grassi (BRA/Virgin-Cosworth)
23. Bruno Senna (BRA/Hispania-Cosworth)
24. Sakon Yamamoto (JPN/Hispania-Cosworth)
