Steve Smith made his highest Test score but was out one short of a maiden double century as Australia were dismissed for 399.
Fast bowler Jerome Taylor was the pick of the West Indies attack, with career-best figures of 6-47 from 25 overs.
The Windies lost three wickets within the first 12 overs of their reply, only Jermaine Blackwood (51) passing 30.
Smith, who resumed on 135 with his team on 258-4, is only the eighth batsman in Test history to be dismissed for 199 and the first since England’s Ian Bell in 2008.
The 26-year-old hit the first two balls of the afternoon session for four and appeared set to become only the third Australian, after Neil Harvey and Steve Waugh, to make a double century at Sabina Park when he was lbw and the ninth wicket to fall.
Having struck three times before tea, Australia claimed their fifth wicket of the evening session with final ball of the day.
Jason Holder had an lbw decision by umpire Ian Gould off Mitchell Johnson overturned earlier in the over but the Australian pace bowler then had a successful review of his own when Veerasammy Permaul was given out caught behind.
Michael Clarke’s team won the first match of the series in Dominica by nine wickets and are on course for a fourth successive series win in the Caribbean.
They begin their defence of the Ashes against England in Cardiff on 8 July.
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