Australia removed Chris Gayle but their normally reliable catching let them down as West Indies made a confident start on Sunday in chasing 475 to win the third and final Test.
At the break, West Indies reached 99 for one in their second innings with Xavier Marshall not out on 42 and vice-captain Ramnaresh Sarwan not out on 18 on the fourth day at Kensington Oval.
Australia made such a belated decision to declare their second innings on 475 for five that the session after lunch started almost 15 minutes late.
The Aussies created a number of chances to put West Indies under early pressure, but three chances were dropped.
Brett Lee suffered twice in his opening spell, when third slip fielder Simon Katich dropped Marshall on one, and mid-off fielder Beau Casson dropped Gayle on eight before Stuart Clark then saw wicketkeeper Brad Haddin drop Marshall on 22.
Australia got a second chance to remove Gayle early, when the left-handed opener was fortunate to survive a run-out chance.
Marshall played Mitchell Johnson to mid-wicket, and Lee missed a direct hit at the bowler's end with Gayle having given up and beyond the point of no return.
But the Aussies did not have to wait long before they removed the West Indies captain, since Gayle mistimed a pull off the hip and was caught at mid-on off Clark for 26 to leave West Indies 64 for one.
Sarwan joined Marshall about 40 minutes before tea and they navigated the West Indies safely to the break with little or no drama.
Before lunch, an unbroken stand of 79 for the sixth wicket between Michael Clarke and Haddin helped Australia to boost their lead.
At the interval, Australia, leading by 35 runs from the first innings, reached 439 for five in their second innings with Clarke not out on 48 and Haddin not out on 45.
Haddin joined Clarke, after Australia lost the wickets of Simon Katich and Andrew Symonds to left-arm spinner Sulieman Benn inside the first hour to leave the visitors on 360 for five.
Benn was the most successful West Indies bowler with three wickets for 147 runs from 47 overs.
Australia suffered a setback to their plans for free scoring in the morning period, after they continued from their overnight total of 335 for three.
Katich was caught at cover for 157 playing a loose drive at his flighted 330th delivery outside the off-stump to bring his marathon eight-hour innings to an end.
Andrew Symonds has been a thorn in the West Indies' side throughout the series, but Benn poached him in his next over, when he had him caught at cover for two also essaying a loose drive.
But Clarke and Haddin batted purposefully to consolidate Australia's position and allow Ponting to make his third declaration in the last four innings of the series.
Australia lead the three-Test series 1-0, after they won the opening Test at Sabina Park in the Jamaica capital of Kingston by 95 runs.
The second Test at the Vivian Richards Cricket Ground in the Antigua village of North Sound was drawn.
The Aussies have already retained the Frank Worrell Trophy.