The SCG pitch lived up to its reputation as being spin-friendly with Nathan Lyon and Steve O'Keefe shared three wickets to justify the hosts' decision to play two specialist spinners for a home test for the first time since 2006.
Opener Kraigg Brathwaite made a resilient 85 to provide almost lone resistance for the tourists on a day when 15 overs were lost to passing showers.
Carlos Brathwaite (35 not out) and Denesh Ramdin (23 not out) shared an unbeaten stand of 48 runs for the seventh wicket to lift the West Indies past 200 after winning the toss and electing to bat.
The innings fell away disappointingly after a promising opening session by the West Indies, who lost both the first two test of the three-test series.
Shai Hope (9), a late selection for the injured Rajendra Chandrika who injured a groin in the warm-up, was the only wicket to fall in the opening session, caught behind off Josh Hazelwood (1-35).
Kraigg Brathwaite and Darren Bravo put on 91 for the second wicket, but Australia took the initiative in the 37 minutes between the start of the second session and a rain interruption.
James Pattinson (1-35) enticed Bravo into an uncontrolled hook which was caught by Usman Khawaja at deep square leg, and the visitors compounded the setback in near comical fashion when Marlon Samuels was run out for four in the final ball before the near two-hour rain delay.
Samuels pushed a Lyon delivery to point and set off for a run. Brathwaite, however, caused confusion as he slipped in the middle of the pitch, dropped his bat and scrambled back toward the non-strikers end, leaving Samuels stranded mid-pitch. Hazlewood made the short throw to Peter Nevill who completed the runout.
Australia 54-2 at stumps to trail Sri Lanka by 227