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.
Russell also won Saturday's qualifying and started in pole position on Sunday.
"It was the kind of race we had expected - chaotic start, difficulty matching the battery and a bit of a yo-yo during the overtaking," says Russell.
Hamilton frustrated
The decisive moment in the battle between Mercedes and Ferrari was the pit stop. Both Mercedes cars made an early stop when the safety car was out, but both Leclerc and teammate Lewis Hamilton stayed out on the track.
"At least one of us should have gone in," seven-time world champion Hamilton was heard saying on the team radio in frustration.
Hamilton finished in fourth place. Lando Norris, McLaren - who took home the overall title last year - was fifth.
Half-Swedish Arvid Lindblad, who competes for Great Britain and Racing Bulls, scored four points in his F1 debut. The 18-year-old finished in eighth place.
Sunday’s race also featured drama when home favorite Oscar Piastri from McLaren crashed out 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.
New rules
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.
Corrected version: In a previously sent version, Arvid Lindblad was attributed to the wrong stable.
