Team mate Lewis Hamilton recovered from a nightmare start to finish second, while Sebastian Vettel – who led into Turn 1 and looked very much in charge prior to the red flags – had to settle for third after 57 laps of Albert Park.
Local hero Daniel Ricciardo took a popular fourth place for Red Bull, well clear of the Williams of Felipe Massa, while Romain Grosjean gave the all-new Haas team points on their debut with sixth.
Force India’s Nico Hulkenberg, Williams’ Valtteri Bottas, and the Toro Rosso duo of Carlos Sainz and Max Verstappen completed the top ten, with Renault’s Jolyon Palmer narrowly missing out on a point in his maiden Grand Prix.
McLaren's Alonso and Haas's Esteban Gutierrez meanwhile were thankfully able to walk away from a huge crash at Turn 3 which caused the red flags to fly on lap 19.
Up until that moment it was Ferrari who held the cards, Vettel and Raikkonen having burst between the two Silver Arrows to snatch a one-two away from the start.
Hamilton got the worst of it, his slow start compounded by losing further ground and positions - and possibly some front wing endplate - in the opening turns, with Verstappen and Massa both able to pick him off and push him from pole to seventh.
That dynamic would all change. Following a 20-minute break to clear the debris from Alonso and Gutierrez's crash, the race restarted with Ferrari still on an aggressive two-stop strategy of using supersoft tyres. Mercedes though had gone conservative and selected the mediums, meaning Ferrari would need to pit again and Mercedes wouldn't. Game on.
It was soon clear that Vettel was not going to open up the 24s gap that he needed for a final stop, and when that came - from supersofts to softs - on the 35th lap, Rosberg, Hamilton and a feisty Ricciardo overtook the Ferrari. Hamilton closed in on the Red Bull and overtook for second place on the 42nd lap, but couldn't make serious inroads into Rosberg's 10s lead.
The Briton's attention instead went on protecting his position as Vettel closed in. With seven laps to run the pair were split by just half a second - but try as he might Vettel could not engineer a move, with his challenge failing two laps from the end when he ran deep and onto the grass at the penultimate turn.
Like Vettel, Ricciardo also bolted on fresh tyres - in his case the supersofts - and flew late on, the Australian setting the fastest lap and rising up to fourth, just missing out on becoming the first Australian to claim a Grand Prix podium on home soil.
Massa was an uneventful fifth, while behind Grosjean sprang a sensation in sixth, giving Haas points in their debut race.
Toro Rosso provided plenty of drama as Sainz and Verstappen quarrelled with each other, and with a host of other cars. It was not always a happy affair, with Verstappen angered by the team's decision to pit Sainz first, and then to not instruct him to move aside. The pair even made very light contact in Turn 15 a few laps from the end, with Verstappen spinning as a result. He caught back up to Sainz by the chequered flag, although neither was able to find a way past Bottas or Hulkenberg.
Palmer's very convincing debut for Renault saw him finish 11th, ahead of team mate Kevin Magnussen who lost time with a puncture on the opening lap but made it up when the race was red flagged and restarted.
Sergio Perez was 13th for Force India, while Jenson Button looked good early on but faded to 14th for McLaren. Felipe Nasr could not repeat 2015's fifth place for Sauber and finished 15th as team mate Marcus Ericsson retired with transmission problems, while rookie Pascal Wehrlein - who made a sensational start to run 15th for a while - was the last of the classified runners in 16th.
There were several retirements - besides Alonso and Gutierrez, Red Bull's Daniil Kvyat hit problems and retired even before getting to the grid, while Manor's Rio Haryanto went out with driveline problems and Raikkonen retired soon after the restart with suspected turbo failure which led to a spectacular fire in his Ferrari's airbox.
WATCH: Race highlights from Australia