Antonelli finished 2.974 seconds behind Russell. Ferrari's Charles Leclerc finished third.
"I feel fantastic. It was a hell of a fight at the start. We knew it was going to be a challenge," George Russell told Sky Sports.
It was the kind of race we had expected - chaotic start, difficulty managing the battery and a bit of a yo-yo during overtaking.
Russell also won Saturday's qualifying.
Half-Swedish Arvid Lindblad, who competes for Great Britain and Red Bull, finished in eighth place. Lando Norris, McLaren - who took home the overall title last year - finished in fifth place.
Sunday’s race also featured drama when home favorite Oscar Piastri from McLaren crashed out of the race even before the start.
Audi's Nico Hülkenberg also failed to start. Red Bull's Isack Hadjar had to retire after eleven laps and Valtteri Bottas, who drives for the new addition, Cadillac, also retired.
The cars are both smaller and lighter this year, as the F1 world undergoes what can be described as a rules revolution. The cars have a completely new powertrain and must run on 50 percent combustion and 50 percent electricity.
After Melbourne, the season continues with races in China and Japan. There are also concerns ahead of the races in Bahrain and Saudi Arabia in April, given the war in the Middle East.
Mohammed Ben Sulayem, president of the international automobile federation FIA, says that "safety and health" will be crucial in decisions regarding the competitions.
