Starting seventh on the grid, Hulkenberg managed to hold on to his position despite facing some tough challenges in the opening laps, and finished the race 50.7 seconds behind fellow German Nico Rosberg of Mercedes, who led from start to finish to win the season opener at the Albert Park.
However, the lady luck did not smile on Hulkenberg's teammate Sergio Perez, who stopped just short of pocketing points in his debut for Sahara Force India.
Rosberg, meanwhile, took the chequered flag 24.5 seconds ahead of Australia's Daniel Ricciardo in his Red Bull debut. But Ricciardo faces the risk of disqualification from second place over fuel rules.
Kevin Magnussen, 21, became the first Danish driver ever to reach the podium by securing a brilliant third place in his Formula One debut for McLaren.
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Jenson Button finished fourth in the second McLaren, while two-time world champion Fernando Alonso of Ferrari was fifth ahead of Williams' Valtteri Bottas, Hulkenberg and Kimi Raikkonen in the other Ferrari.
This year Formula One has shifted to quieter, turbocharged 1.6-litre V6 engines with hybrid components and a limit on fuel and the rate of fuel use.
Only 14 cars out of 22 finished the race in the eventful race, which witnessed a collision between Felipe Massa and Kamui Kobayashi in the opening lap, thus drawing curtains to their run before it had started.
Hulkenberg, meanwhile, was delighted with his start to the season, which incidentally was the German's maiden finish at the Albert Park here.