The Mercedes driver, on wet tyres, knocked Vettel's Red Bull team-mate Daniel Ricciardo, who was on intermediate rubber, off top spot by three tenths of a second in the final seconds of a rain-hit session.
Nico Rosberg, who had briefly taken first place before Hamilton and Ricciardo improved late on, was third ahead of McLaren's rookie Kevin Magnussen.
Toro Rosso's Jean-Eric Vergne showed his wet weather prowess with a superb sixth place ahead of Force India driver Nico Hulkenberg, both setting their times on intermediates.
Behind the pair was debutant Daniil Kvyat, who impressed despite an off in Q3 on the run between Turns 10 and 11.
He took eighth place on wet rubber, ahead of Williams drivers Felipe Massa (intermediates) and Valtteri Bottas (wets), although the latter must serve a five-place grid penalty for a gearbox change before qualifying.
Several of the drivers who failed to advance from Q2 to Q3 were unable to improve thanks to yellow flags caused by Kimi Raikkonen's late crash as rain returned in intermediate conditions.
The Ferrari driver lost the rear at the exit of Turn 3 and spun into the wall, with Vettel among those who were attempting to jump into the top 10 at the time.
With both failing to make the cut in 12th and 13th, Jenson Button made it three world champions to fail to make the top 10 shootout in 11th.
Sauber's Adrian Sutil, Caterham's Kamui Kobayashi and Force India driver Sergio Perez, who ran through the gravel at Turn 2 on his final flying lap, also fell in Q2.
Marussia driver Max Chilton was the fastest of the drivers to be knocked out in Q1, which was effectively ended at a point when most had managed only one run thanks to rain at the halfway mark.
Chilton was just 19 thousandths of a second slower than Kobayashi, who did make the cut but was unable to do better than 15th in the second stage of qualifying.
Chilton's eam-mate Jules Bianchi, Sauber's Esteban Gutierrez (who will be hit with a five-place penalty for a gearbox change) and Caterham rookie Marcus Ericsson were also eliminated in Q1.
Joining them were the two Lotus E22s of Romain Grosjean and Pastor Maldonado, the latter not able to attempt a lap until the damp conditions late on and having two off-track excursions before aborting his run.
Australian Grand Prix starting grid
1. Lewis Hamilton (Britain) Mercedes
2. Daniel Ricciardo (Australia) RedBull - Renault
3. Nico Rosberg (Germany) Mercedes
4. Kevin Magnussen (Denmark) McLaren
5. Fernando Alonso (Spain) Ferrari
6. Jean-Eric Vergne (France) Toro Rosso - Renault
7. Nico Huelkenberg (Germany) Force India - Mercedes
8. Danill Kvyat (Russia) Toro Rosso - Renault
9. Felipe Massa (Brazil) Williams-Mercedes
10. Jenson Button (Britain) McLaren
11. Kimi Raikkonen (Finland) Ferrari
12. Sebastian Vettel (Germany) RedBull - Renault
13. Adrian Sutil (Germany) Sauber - Ferrari
14. Kamui Kobayashi (Japan) Caterham - Renault
15. Valtteri Bottas (Finland) Williams-Mercedes
16. Sergio Perez (Mexico) Force India - Mercedes
17. Max Chilton (Britain) Marussia - Ferrari
18. Jules Bianchi (France) Marussia - Ferrari
19. Marcus Ericsson (Sweden) Caterham - Renault
20. Romain Grosjean (France) Lotus - Renault
21. Esteban Gutierrez (Mexico) Sauber - Ferrari
22. Pastor Maldonado (Venezuela) Lotus - Renault
- Sports & Recreation
- Motor Racing
- Daniel Ricciardo
- Nico Rosberg
- Fernando Alonso
- Kamui Kobayashi