Vettel's early exit ended the Red Bull driver's record run of nine successive victories racked up since last August.
While one German smarted, another celebrated as 28-year-old Rosberg capitalised on a brilliant start from third on the grid, snatching the lead before the first turn and roaring to a 24.5-second victory ahead of Red Bull's Australian Daniel Ricciardo.
On an overcast day at Albert Park, Danish rookie Kevin Magnussen shone with a brilliant third place finish for McLaren, emulating Hamilton's first effort for the British team at the same Grand Prix in 2007.
The result meant all three men on the podium had beaten world champion team mates in a stunning triumph of the underdogs.
Rosberg, tipped to duel with team mate Hamilton for the championship, celebrated his fourth race victory and first since last year's British Grand Prix, when he was also the beneficiary of technical mishaps to Hamilton and Red Bull's Vettel.
"Brilliant stuff, what a car you've given me! What a car!" the thrilled German said over the team radio after crossing the line.
"The car was just really, really quick today," the German later told reporters, looking forward with relish to the next race in Malaysia in two weeks.
"A really good engine, not much problem with fuel consumption. It just all worked perfectly."
The gaping margin of victory underscored Mercedes' superior preparations for F1's technical revolution, which saw all teams struggle during winter testing with the new V6 turbocharged hybrid engines.
The glitches continued as only 14 of the 22 cars finished on a gusty day at the bumpy street circuit which was doused by a brief rain-shower early in the race.
Hamilton, who snatched pole position at the end of a wet qualifying session on Saturday, noticeably lacked power on his start and was called in by his team to retire on the third lap.
Mercedes later clarified his car had suffered a misfiring cylinder. "We will recover from this, it's only a small hiccup. There's a long way to go still," Hamilton told Sky television.


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