On an overcast day at Phillip Island, the Aprilia-Trackhouse rider benefited from two long lap penalties served by a flying Marco Bezzecchi to take the chequered flag 1.418sec clear of Ducati's Fabio Di Giannantonio.
Aprilia's Bezzecchi, who won the 13-lap sprint on Saturday, came third, 2.410sec adrift, to fill out the podium.
KTM's Pedro Acosta was fifth ahead of Luca Marini on a Honda and Yamaha's Alex Rins, while Spanish rookie Fermin Aldeguer, who won the MotoGP in Indonesia a fortnight ago, finished 14th.
"I cannot believe it," said Spain's Fernandez, who had never been on the podium before.
"The team never stopped supporting me, and this is a consequence of hard work. I managed the rear tyre throughout the race.
"The last five laps seemed super long. Thanks to everyone who supported me."
While Fernandez, who started fourth, stole the glory, Marquez all but sealed runner-up spot to his injured brother Marc in the world championship with three races to go.
The Spanish Gresini rider's fourth earned him 13 points to be 97 clear of Bezzecchi with a maximum 111 at stake in the final three meetings of the 22-stop year -- in Malaysia, Portugal and Spain.
Ducati's two-time world champion Francesco Bagnaia crashed out with four laps left to cap a miserable weekend.
He struggled in every session with unexplained shaking of his bike, a problem he also experienced in Indonesia after winning both the sprint and grand prix in Japan a week earlier.
With no points to show, he has slid behind Bezzecchi to fourth in the standings.
Marc Marquez was crowned world champion in Japan, but is not in Australia after Bezzecchi slammed into him in Indonesia, an incident that left the Spaniard needing shoulder surgery.
Bezzecchi was slapped with a double long lap penalty -- essentially five-to-six seconds -- to be served Sunday for causing the accident, and it cost him victory.
"It was a super tough race, with the penalty," he said.
"But my strategy worked perfectly, a good start and then pushing hard at the beginning.
"I didn't imagine I could get a podium with this penalty."
Bezzecchi stormed clear at the opening corner, and by the end of lap one was leading from Fernandez and Acosta, with polesitter Fabio Quartararo down to fourth.
The Italian opened a 1.2sec gap before taking his first penalty on lap five, emerging in third.
He took the second the following lap, coming back in sixth with a 2.8sec gap to leader Fernandez which slowly got bigger as Bezzecchi got stuck in traffic.
By lap 10, Fernandez was pulling clear of Acosta, a lead he built on as the race progressed with an expected counter-attack from Bezzecchi not materialising.
Home hope Jack Miller, who started from third, crashed out early in the race, as did Frenchman Johann Zarco and Spain's Joan Mir.
