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Roseau: Cowan (55) and Ponting (57) scored useful half-centuries as Australia ended Day 3 at 200/6, leading by 310 runs. Roach, Deonarine and Shillingford picked up two wickets each.
West Indies had looked to have got back into the match having added some important runs in the morning session before being bowled out for 218 and then took two quick wickets with David Warner going just before lunch and the dangerous Shane Watson just after the resumption.
The hosts total owed much as ever to a typically stubborn innings of 68 by veteran Shivnarine Chanderpaul.
West Indies had been 165/8 overnight with Chanderpaul and Ravi Rampaul having already put on 45 for ninth wicket.
They took their partnership to 66 before Nathan Lyon broke through. Rampaul came down the wicket but got a thick outside edge and the ball flew up to Warner at point.
The visitors took the new ball after 83.1 overs and in the end it was Chanderpaul that fell.
Mitchell Starc was bringing the ball back in off the seam and one finally got past the obstinate West Indian's bat and trapped him lbw.
Chanderpaul had faced 164 balls for his 68 to make him the highest scorer in the series with 277 runs at an average of 92.33.
It left Australia to face a tricky five overs before lunch and the West Indies got the breakthrough that they would have wanted.
Warner had already struck Rampaul for two boundaries. However, in the last over before the interval he drove loosely at a Kemar Roach delivery and edged to the only fielder in the slip cordon, Chanderpaul.
Shane Shillingford, who had taken six wickets in the first innings, came on to bowl straight after lunch.
Michael Hussey (17) and Ryan Harris (4) took Australia to stumps without any further scares.
Brief scores
Australia 328 (Wade 106, Shillingford 6-119) and 200 for 6 (Ponting 57, Cowan 55)
West Indies 218 (Chanderpaul 68, Lyon 4-69)
Status Australia lead by 310 runs
