The Briton recorded a fastest lap of one minute 26.327 seconds, trouncing Rosberg by nearly six-tenths of a second while leaving the Williams of Felipe Massa well adrift in third.
Hamilton set the early running in the final session before roaring home to capture his 39th pole on a windy afternoon at Albert Park.
"It's been a great start to the weekend," Hamilton told reporters after capturing his first pole since the Russian Grand Prix last October.
"A big rush and a huge effort from all the guys back at the factory to enable us to come here and have this performance so I feel incredibly blessed to have this car."
The two-time world champion's pole was Mercedes' 12th in succession and victory in Sunday's race would appear a formality for the team that raffled 16 of last year's 19 race wins.
Rosberg led Hamilton in two of the three practice sessions but locked up and spun into the grass in the final qualifying phase after complaining of an engine cut-out in the second.
However, last year's championship runner-up blamed himself for being off Hamilton's pace.
"It wasn't a great day today," he said. "For me, the speed was there. I just didn't get it together."
Four-times world champion Sebastian Vettel will start fourth on the grid on his debut for Ferrari with his Finnish team mate Kimi Raikkonen fifth.
Valtteri Bottas will start sixth in the other Williams, although the Finn will rue an error on the final straight that denied him a chance of claiming a spot on the second row.
Though the sessions produced no major incidents, team radios blared throughout as drivers reported a myriad technical problems and occasionally skidded off track.
McLaren's dismal weekend continued after troubled winter testing, with Jenson Button and Kevin Magnussen to line up from the back of the grid after failing to be in the top 15 cars that advanced through to Q2.
Red Bull are also well off the pace and Australian Daniel Ricciardo complained from the outset that his car lacked power.
He will line up seventh on the grid while his Russian team mate, Daniil Kvyat, was knocked out in Q2 and will start 13th.
Having fought legal battles with Giedo van der Garde all week, Sauber's nominated drivers Marcus Ericsson and Felipe Nasr qualified after the Dutchman elected not to pursue his racing seat at Albert Park.
Swede Ericsson was eliminated in Q1 and will start 16th on the grid in front of the McLarens with his Brazilian team mate five spots ahead.
Only 18 cars will compete in Sunday's race after Manor Marussia were unable to put Spaniard Roberto Merhi and Briton Will Stevens on the track for either qualifying or any of the three practice sessions.
(Editing by John O'Brien)
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