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The Socceroos had drawn their previous two qualifiers in November, after a 2-1 reverse to Japan in October, leaving them outside the automatic qualification spots in Group B.
However, they got their bid for a place in Qatar back on track in style on Thursday in Melbourne, inflicting an eighth successive qualification defeat on Vietnam in the process.
Tom Rogic thought he had put Australia ahead inside the opening 20 seconds, only for VAR to disallow the goal for Jackson Irvine straying offside.
Vietnam got no such reprieve when Jamie Maclaren headed home from Rogic's cross in the 30th minute, with the Celtic midfielder turning from provider to scorer on the stroke of half-time.
Slack defending gifted Australia a third when Craig Goodwin latched onto Mat Ryan's pass in the 72nd minute to score his first international goal, before Riley McGree picked out the bottom-right corner to make it 4-0, also his first strike for his country.
It was just the second time the nations have met in World Cup qualifying, with Australia – who are back to within two points of group leaders Saudi Arabia – making things rather easier for themselves this time after a 1-0 win in the first match.