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The season-opener was scrapped hours before the first practice session was due to get under way after a McLaren team member tested positive to the virus.
Ferrari's Sebastian Vettel was runner-up, ending Mercedes's run of five successive one-two finishes, with Hamilton's team mate Valtteri Bottas third.
The Briton took an extra point for the fastest lap of the race.
The win was the 75th of Hamilton's career, second in a row after his lucky triumph in Bahrain two weeks ago, and sixth in China.
It was Hamilton's seventh win in 10 races this season and 80th of his career.
The Mercedes driver triggered initial concern when he started a series of posts by saying he felt like 'giving up on everything.'
The result also left only Bottas capable of challenging Hamilton, who saw his lead narrow to 64 points, in the overall standings.
Hamilton's absence from Britain's New Year's honours list has angered his Formula One fans and triggered fresh debate about the sport's status and whether the six-time world champion is sufficiently appreciated at home.
Lewis Hamilton is now only seven wins short of Michael Schumacher's all-time record of 91.
The five-times world champion now has 79 career wins, 12 short of Michael Schumacher's all-time record with 13 races remaining this season.
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