Offspinner Kevin Sinclair (50) and veteran paceman Kemar Roach (eight) added 31 for the ninth wicket after the visitors resumed at 8-266 on Friday.
The stand was broken when Roach called for a single but Sinclair wasn't interested.
Roach slipped over mid-pitch and Marnus Labuschagne underarmed to wicketkeeper Alex Carey with Roach stranded.
Kemar Roach (right) falls over and is run out on the second day of the Test match at the Gabba. (Jono Searle/AAP PHOTOS)
Sinclair struck a four and a straight six off Nathan Lyon to reach his half-century, but was stumped next ball.
Roach and Sinclair were untroubled for most of the first hour, but Australia missed a trick when Cameron Green dropped Sinclair in the gully when he was on 30.
Pat Cummins drew the edge but Green, usually so reliable, watched in dismay as the ball went in and out of his bucket hands.
Australia set defensive fields, with even Cummins employing a deep point.
Sinclair was cool as a cucumber on debut, but his first-class record suggests he is no mug with the bat.
The 24-year-old now boasts nine first-class half-centuries, with a highest score of 86.
The West Indies did well to recover from 5-64 to set Australia a competitive total.
No.5 batter Kavem Hodge (71) and wicketkeeper Joshua Da Silva (79) were the stars on day one.
Left-armer Mitchell Starc (4-82) was the pick of the Australian bowlers.
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