Indonesia had not beaten Australia in 43 years and, despite the south-east Asian side's loud supporters vastly outnumbering the Australian fans in the tiny arena, it was Graham Arnold's side who prevailed when they converted their chances.
Indonesia started the game on the front foot and gave their opponents an early scare with an effort on goal but Australia took the lead in the 12th minute when Jackson Irvine's cross was deflected into the net by defender Elkan Baggott.
Australia weathered the storm as Indonesia attempted to find a way through their staunch defence, before Martin Boyle gave them a two-goal cushion on the stroke of halftime when he connected with Gethin Jones's cross to head in at the far post.
The Indonesian fans in red and white tried their best to spur on their team but Australia remained composed, although they nearly found themselves in trouble when Jones deliberately tripped Rafael Struick off the ball in retaliation.
The foul occurred right in front of Arnold, who angrily threw a water bottle to the turf expecting a red card. But the referee only cautioned Jones, who was immediately taken off by Arnold.
Craig Goodwin came on as a late substitute and the forward made an instant impact when he pounced on a rebound to score in the 89th minute while towering defender Harry Souttar made it 4-0 moments later with a glancing header from a set piece.
Australia will play either Saudi Arabia or South Korea in the quarter-finals.
