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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.
Hamilton is now 17 wins short of Michael Schumacher's all-time record of 91.
Starting second behind pole-sitter Hamilton, Bottas got the jump on the Briton during a typically messy start at Albert Park and ended up cruising to his fourth win by some 20.80 seconds after delaying a tyre-change.
The Briton, who started his career working for the Hesketh team in 1977, died in Melbourne of a pulmonary embolism.
British American Tobacco, which had its own Formula One team before selling to Honda in 2006, is returning to the sport under a multi-year global partnership with McLaren.
The chassis name was listed as Racing Point, with the company name Racing Point UK Limited.
It was the 11th victory of the year for Hamilton, who dominated the race with a controlled drive.
Hamilton had needed only five points to be sure of the title while four times champion Vettel had to win to have any hope of denying the Briton.
The Formula One team finally confirmed on Thursday that Perez would continue racing for them in 2019.
No woman has competed in Formula One since 1976, but organisers of the 'W Series' hope to provide a platform for them to develop skills before taking on the men further up the motorsport ladder.