A Noah Botic brace either side of half-time was enough to nab the Joeys all three points and passage through to the round of 16 in third place, while Ecuador snatched second after a late 3-2 victory over Group B rivals Hungary.
Leaders Nigeria maintained top spot despite their defeat, but will rue a host of missed opportunities against Trevor Morgan's side.
The Joeys had made a habit of slow starts in Brazil and, were it not for goalkeeper Adam Pavlesic, would have fallen behind yet again on Saturday after an early barrage from the Africans.
Nigeria's intentions set the tone for a fast-paced encounter at the Bezerrao and it didn't take long before the Joeys made them pay; Caleb Watts the architect of a swift 13th-minute counter-attack completed by the in-form Botic.
Australia's early ascension, however, only served to motivate their opponents and they soon responded midway through the first half through Peter Olawale's clever turn and finish.
Nigeria's persistent pressure only heightened in the second half and almost paid off after Olakunle Olusegun's driven effort left Pavlesic beaten, only to be denied by the base of the post.
Morgan had set his side out to utilise both speed and space in transition and, in the 54th minute, it paid dividends once again.
With Watts bursting through midfield and into enemy territory, a well-timed touch inside the box drew contact and left referee Istvan Kovacs with no choice but to point to the spot.
And with Botic already on three goals for the tournament, the ever-confident forward soon obliged for his fourth, sending Joseph Oluwabusola the wrong way with ease.
Australia's restored advantage spurred one last fightback from their opponents, but Pavlesic was again on hand to preserve the precious three points.
