The Briton produced a stunning lap to be 0.360 seconds quicker than Mercedes team-mate Nico Rosberg - and seemed as if he may have been able to go faster.
But the track was empty for the final five minutes and senior figures said the format should be rethought.
Red Bull team boss Christian Horner said F1 should "apologise to the fans".
"It didn't really work for me," Horner added. "We have not really put on a show.
"To have Sebastian Vettel and Kimi Raikkonen in fast cars not taking part with five minutes to go is wrong."
Rosberg was behind both Ferraris after the first runs in the final session, but he grabbed second on his final run ahead of Vettel and Raikkonen, who will start third and fourth respectively.
The first race of the new season gets under way on Sunday at 05:00 GMT, with coverage on radio 5 live from 04:00 and online from 03:30.
Rosberg said straight after the session: "It's good to try something but it hasn't worked - so we should go back."
Ferrari's Vettel, who qualified third but was able to change out of his overalls in time for the post-qualifying news conference because he did not run in the second part of the final session, said: "I don't see why everyone is surprised it didn't work.
"It is a bit busier at the beginning of the session but for no reason. People want to see us pushing to the limit at the end of the session. It is the wrong way to go and that's what we said."
The new format did work on one level, however. It made the first and second parts of the session more fraught - and one top team was caught out as Red Bull's Daniil Kvyat ended up 18th on the grid.
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Hamilton was 0.838secs quicker than Ferrari's Sebastian Vettel, who was also 0.478secs behind Rosberg.
The margin between the cars was such that Ferrari decided not to bother doing a second run in the final session of qualifying because they accepted they could not beat the Mercedes and preferred to save a set of tyres for the race.
On the face of it, that suggests Mercedes are as far ahead of Ferrari as they were last year.
But Hamilton was actually even further ahead of Vettel in qualifying in Australia last year and the German won the next race in Malaysia.
Hamilton said: "I really have to take my hat off to this team - what they have done to raise the bar once more. It inspires and motivates me.
"I enjoyed driving the car in qualifying, got the set-up just right. They were some sexy laps, beautiful rhythm, it felt so good. I felt like James Brown at the end of the lap."
Vettel added: "We expected them to be stronger in qualifying, which they were. Very happy with the lap in the end so we saved a set for the race. We still have high hopes for tomorrow and it is a long year."
Toro Rosso's Max Verstappen and Carlos Sainz were fifth and seventh, split by Williams driver Felipe Massa.
Red Bull's Daniel Ricciardo and the Force Indias of Sergio Perez and Nico Hulkenberg completed the top 10.
McLaren's Fernando Alonso and Jenson Button took 12th and 13th, a huge improvement on their dismal 2015, and Briton Jolyon Palmer 14th for Renault on his grand prix debut, ahead of team-mate and former McLaren driver Kevin Magnussen.
Australian GP qualifying results
Australian GP coverage details
Lewis Hamilton took pole position for the season-opening Australian Grand Prix as the new elimination qualifying format came in for heavy criticism.