Reigning world champion Hamilton led from the start to the chequered flag, beating last year’s winner Rosberg by 1.3 seconds, with Sebastien Vettel third in his Ferrari debut.
Only 11 cars finished the race after mechanical problems and an injury to Valtteri Bottas left just 15 on the starting grid — the lowest number for a year-opener since 1963.
And Max Verstappen’s record-breaking debut at the age of 17 years and 166 days ended on a sour note when his Toro Rosso suffered a power unit failure on the 34th lap.
At the front, Mercedes were in ominous form with Hamilton finishing a whopping 34 seconds in front of Vettel, indicating a tough year ahead for the Silver Arrows’ rivals.
It was Mercedes’ eighth straight victory, dating back to Belgium last August, and their 20th race in a row with at least one driver on the podium.
Hamilton, 30, has now won seven of the last eight races and 34 from 149 grands prix, although this was his first in Australia since 2008.
“Nico was quick throughout the race,” he said of his fierce rival. “In terms of tyres we did not know how far they could go. When Nico turned up the heat I was able to react which was good.”
Rosberg, who will have much to ponder after pole-sitter Hamilton’s supreme opening week, insisted it was a “nice feeling to be second”.
“Lewis has done a fantastic job, he drove like a world champion all weekend. I’ll give my maximum and try to beat him all year,” he said.
Four-time world champion Vettel yelled “Forza Ferrari!” as he celebrated a morale-boosting podium finish on his debut for the team after switching from Red Bull.
Ferrari finished only fourth in last year’s constructors’ championship and Vettel, who beat Williams’ Felipe Massa to take third place, was all smiles as he collected his trophy.
“We can be very proud. We have a great car, there is a lot of work ahead of us to beat these (Mercedes) guys,” Vettel said. “We want to make sure that life is not easy for these two during the season.”
Brazilian Felipe Nasr finished a plucky fifth on his F1 debut in a boost to his Sauber team, entangled all week in a distracting legal battle over their driver line-up.
But Australia’s Daniel Ricciardo emphasised Red Bull’s current struggles when he finished sixth.
– ‘I’ll be back’ –
With fledgling team Manor unable even to take part in qualifying, the race lost another driver when Williams’ Bottas was ruled out with a back injury.
Red Bull’s Daniil Kvyat and McLaren’s Kevin Magnussen then withdrew with mechanical problems on the reconnaissance lap, leaving a sparse grid of only 15 cars.
Hamilton got away quickly off pole and was first into the right-hand hairpin but Lotus’s Pastor Maldonado was sideswiped into the barriers and crashed out as the safety car came out on the opening lap.
When the safety car withdrew, Hamilton opened a stunning 2.4sec gap over team-mate Rosberg by the end of the first racing lap.
But Rosberg put in some fastest laps to reduce the gap to 1.2secs behind Hamilton after 10 laps, with Massa and Vettel eight to nine seconds adrift.
At one-third distance, Hamilton led Rosberg by 2.4sec, with Massa 1.5sec clear of Vettel in the battle to join the Mercedes on the podium.
Both Mercedes had a one-stop strategy. Rosberg got the faster pit stop by 2.9sec but Hamilton was able to retake the lead with ease in the race to the chequered flag.
Ferrari’s Kimi Raikkonen retired on lap 42 moments after his second pit stop, when he drove off with the left rear wheel not properly attached.
Three-time race winner Jenson Button battled on with his misfiring McLaren to finish just out of the points in 11th — but also in last place in the reduced field.
There were cheers when Hollywood star Arnold Schwarzenegger awarded the trophies at the podium ceremony, with Hamilton joking: “I thought you were taller!”
The two-time world champion added: “I’ll be back.”