The hosts moved up to second place in Asian qualifying Group B and know victory at home to Iraq next Tuesday will seal their place in Brazil next summer, alongside pool winners Japan.
Australia went into the match level on points in third place with their opponents, two points behind Oman, and knowing only victory would do.
Mark Bresciano eased any home nerves with the opening goal after 15 minutes and Tim Cahill added a second just after the hour mark.
New Bayer Leverkusen signing Robbie Kruse netted the third in the 76th minute before veteran Lucas Neill completed the scoring six minutes from time.
South Korea strengthened their position at the top of Group A with a 1-0 win at home to Uzbekistan.
Akmal Shorakhmedov's own goal three minutes before half-time decided the contest and left the Koreans needing just a point from their final game against Iran to reach the World Cup.
Indeed, even that might not be necessary. Should Iran lose to Lebanon this evening, South Korea would qualify for Brazil 2014.