Steve Smith guided Australia to a healthy position as they reached 60-2 at stumps on the third day of the second Test against the West Indies in Brisbane on Saturday.

Australia need another 156 runs for victory to take a clean sweep of the two-Test series with eight wickets in hand.

At stumps, Smith was on 33 with a struggling Cameron Green alongside him on 9.

Australia's hopes of taking the win, however, may be hampered by predicted heavy rain for the next two days.

Australia had wrapped up the West Indian second innings for 193 shortly after the tea break when No.11 Shamar Joseph had to retire hurt after being hit on the toe by a Mitchell Starc bouncer.

Joseph was taken for scans on Saturday night and is unlikely to bowl in the second innings.

The West Indies went into the final session six wickets down, but lost the last fours, including Joseph, for just 10 runs.

Chasing 216 for victory, Australia lost an early wicket when Usman Khawaja was caught down the leg side off Alzarri Joseph.

Marnus Labuschagne, who has had a lean summer, failed for the second time this match, edging Justin Greaves to third slip where Kevin Sinclair took a sharp catch to leave Australia 42-2.

On an oppressively hot and humid afternoon in Brisbane, Australia's pace bowlers were forced into three-over spells throughout the day, followed by time off the field to recover.

Every time a dangerous partnership started to develop, Australia managed to take a wicket to keep the deficit in check.

After resuming Saturday at 13-1, West Indies captain Kraigg Brathwaite and No.3 Kirk McKenzie were intent on keeping the Australians in the field as long as possible.

McKenzie in particular looked in great touch as he punished anything loose from the Australian pace attack.

Brathwaite was not as fluent and after scraping his way to 16, he played a poor shot to an innocuous Green delivery and chipped a simple catch to Labuschagne at cover.

However, he and McKenzie had put on a 50-run partnership to lay a good foundation for the visitors.

McKenzie has had a good tour and the stylish left-hander moved comfortably to 41 before he tried to sweep off-spinner Nathan Lyon and was trapped leg before, leaving the West Indies 86-3.

Alick Athanaze and Kavem Hodge consolidated and reached the first break with few troubles.

Lyon struck again after dinner, drawing an edge from Athanaze (35) before a brilliant piece of fielding from Travis Head saw Hodge run out for 29.

Hodge moved forward and played the ball straight to Head at short leg, who flicked the ball onto the stumps and although Hodge's bat was over the line, it had bounced up and was in the air when the stumps were broken.

First innings top-scorer Joshua Da Silva didn't last long, caught by Green on the second attempt off Starc to leave the West Indies 157-6, 179 runs in front.

But any hope of setting a really big target faded with the post-tea collapse.