With the second and third sessions at Melbourne's Albert Park held over from Saturday due to adverse weather conditions, it was reigning three-time champion Vettel who comfortably grabbed the 37th pole of his career.
The 25-year-old German finished four tenths of a second clear of team-mate Mark Webber, who has yet to stand on the podium in his home race, whilst Mercedes new boy Lewis Hamilton was a superb third.
Despite early morning rain, it relented in time for the start of the 15-minute Q2 and the 10-minute blast for Q3, ensuring there were no further delays.
Instead, the calls from the pitwall were all about tyre choice, with McLaren - on behalf of Sergio Perez - getting it spectacularly wrong.
With the track still damp at the start, the obvious call was for the intermediate wet tyre, but as a faint dry line began to develop over the 15-minute session, McLaren gambled on switching to dry supersofts.
Whilst Button realised it was the wrong choice and switched back to intermediates for a final run that got him into the top-10 shoot-out, Perez was left high and dry, resulting in an apology by his team as he starts 15th.
Button, in a car which McLaren team principal Martin Whitmarsh has revealed they are struggling to understand, will start 10th, a place behind fellow Briton Paul Di Resta in his Force India.
Hamilton finished 0.6secs adrift of Vettel to be the best of the rest, followed by the Ferraris of Felipe Massa and Fernando Alonso.
Nico Rosberg in his Mercedes starts sixth, 0.2s down on Hamilton, with the Lotus pairing of Kimi Raikkonen and Romain Grosjean seventh and eighth.
Behind the British pair of Button and Di Resta on row five, Nico Hulkenberg starts 11th for Perez's former team Sauber.
On his first qualifying session for 16 months after a year away from the sport, Adrian Sutil will line up 12th for Force India.
On the seventh row of the grid are Toro Rosso duo Jean-Eric Vergne and Daniel Ricciardo, with Williams rookie Valtteri Bottas 16th, a place behind Perez.
Following Saturday's Q1 that survived the weather, Bottas' team-mate Pastor Maldonado starts 17th ahead of four rookies, led by Esteban Gutierrez for Sauber.
Marussia occupy row 10, with Jules Bianchi ahead of Max Chilton, with the Caterham pair of Giedo van der Garde and Charles Pic on the back row.
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