The first leg had ended goalless and in the second leg, Mile Jedinak converted two penalties in the 71st and 85th minutes to give Australia a 3-1 win.
Australia had taken the lead in the 54th minute due to an own goal from Maynor Figueroa and mounted further pressure on Honduras to earn two penalties.
Honduras responded in the 90th minute through Alberth Elis but it was too late to halt Australia's march.
The quadrennial showpiece in 2018 will be Australia's fourth straight World Cup.
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