Michael Clarke’s side closed day three of the tour match at Chelmsford on 212-8, with only the skipper making a half-century as Australia struggled.
The home side resumed on 299-3 and went on to score 414 in their first innings, with Ravi Bopara completing his century, although pace bowler Mitchell Starc (6-51) offered some encouragement for Australia.
Jesse Ryder (10) was the first wicket to fall as he clipped spinner Nathan Lyon to backward square leg off the bowling of Mitchell Marsh, who then proceeded to dismiss Bopara (107) shortly afterwards as he was caught in the slips.
Ryan ten Doeschate smashed 36 off 33 deliveries, including a six off Lyon, before he was caught behind off Starc and Matt Salisbury then had his stumps removed second ball by the New South Wales quick bowler.
Starc picked up his fifth wicket when James Foster (23) was caught at gully, and with Nick Browne not batting after dislocating a finger in the field, the tail washed off when Tom Moore’s stumps were sent flying by Starc for a seven-ball duck.
Essex went on to make an early breakthrough in the afternoon session when James Porter bowled David Warner for four.
Chris Rogers, hoping to earn a recall to the Test side after being forced to sit out the West Indies tour because of concussion, was caught behind off Salisbury for 32 to leave Australia 58-2.
Adam Voges was trapped lbw by spinner Aron Nijjar for just one and Shane Watson was dismissed the same way in the next over by Ten Doeschate.
Marsh was the next to go after the tea interval when he cut a delivery from Salisbury on to his stumps for 37 and after taking a blow to the hand, Clarke was eventually bowled by Nijjar for 77.
Peter Nevill was then caught in the slips off Bopara for 12, while Starc (13) holed out to mid-off to set up an intriguing final day, with Australia 360 ahead.