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A rampant Germany doubled their advantage after 34 minutes as Gnabry twisted his way around Netherlands defender Virgil van Dijk.
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.
Haris Seferovic scored a hat-trick as Switzerland recovered from conceding two early goals to beat World Cup semi-finalists Belgium 5-2 on Sunday.
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 Briton stands on the brink of becoming only the third man to win at least five titles, with his team's stranglehold on both championships tighter than ever after he won Sunday's Japanese Grand Prix.
Lewis Hamilton held off a mid-race challenge from Red Bull's Max Verstappen to register a record-equalling fourth triumph at the floodlit Marina Bay Street Circuit track
Formula One world champion Lewis Hamilton equalled Michael Schumacher's record of five Italian Grand Prix wins on Sunday and left Ferrari feeling the pain once again in their own backyard.
Vettel is 17 points adrift of Hamilton in the standings with eight rounds remaining and can expect Raikkonen to give him every assistance when race day comes.
The ring-like 'halo' was introduced this season to protect the drivers' exposed helmets.
With this win, Vettel trimmed Lewis Hamilton's Formula One lead to 17 points with eight races remaining.