Spinner Nathan Lyon bagged three wickets as West Indies slumped to 165 for eight to leave Australia with a lead of 163 at the close of the second day of the third test on Tuesday.
Matthew Wade's maiden test century had fired Australia, who lead the series 1-0, to a first-innings total of 328 after they had been 169 for seven at one stage during the first day.
After West Indies off-spinner Shane Shillingford had done the damage with a six-wicket haul, his best ever test performance, it was the turn of Australia's main spinner Lyon to shine as a fragile West Indies top order was exposed.
Opener Kraigg Brathwaite fell without scoring, edging Ben Hilfenhaus to first slip Ryan Harris who gobbled up the ball at the second attempt.
Kieran Powell and Adrian Barath made some solid progress, putting on 61 before the latter, on 29, lobbed up a bat-pad catch to Ed Cowan at short-leg off Lyon.
Shortly before tea, part-time spinner Dave Warner removed Darren Bravo in similar fashion, the left-hander's inside edge coming off his pads and looping up to Cowan.
That was a blow that West Indies failed to recover from in a poor final session for the hosts.
Kieran Powell, who had looked well settled on his way to 40, got a thick inside edge to play on from Lyon and then Harris trapped Narsingh Deonarine leg before for just seven.
Carlton Baugh once again never looked comfortable, the bounce from Lyon doing him as he pushed forward and fed up a simple bat-pad catch to Cowan at short leg.
The home side's problem were not limited to playing spin though.
Skipper Darren Sammy added to his team's troubles when he was run out for 10 and then Shillingford went first ball as he was beaten by a fine inswinger from Mitchell Starc as West Indies looked in danger of following on.
As so often, it was Shivnarine Chanderpaul who provided the resistance. He reached 34 not out by the close, supported well by Ravi Rampaul (24 not out) as a much-needed 45 run partnership gave the hosts some hope.
It was an impressive bowling display by Lyon, well supported by the seamers, but the tone of the day had been set by his side's aggressive batting in the morning session.
Wade made 106 from 146 balls, including 10 fours and three sixes, his positive approach paying off in a 102-run partnership with Hilfenhaus which transformed Australia's first innings.
The early run out of Mitchell Starc (35) offered the possibility of a swift elimination of the tail but, not for the first time, the Australian lower order showed their quality.
Eschewing the cautious approach taken by the top order batsmen on Monday, Wade went on the attack and his partnership with Hilfenhaus came at twice Monday's run-rate with the 102 runs coming from 20.1 overs.
"As has been proven throughout the series, the Australians bat very deep and you are never actually through them," said West Indies assistant coach Toby Radford.
"You think that you are through them - we've got through the top order many times but it has been difficult actually finishing them off."