The hosts' innings was wrapped up swiftly this morning at 257, giving Australia a lead of 54.
They reached 73 for three, 127 ahead, before the second heavy downpour of the day brought an early close with only 30.4 overs having been bowled in the day.
The hosts resumed this morning at 252 for nine and added just five before wicketkeeper Carlton Baugh was trapped lbw by Michael Beer for 31, a decision only given after a DRS review as Baugh missed a sweep at the fourth ball of the day.
Australia openers Ed Cowan and David Warner extended their side's lead to 80 - although the former was dropped at slip by Windies captain Darren Sammy before he had scored.
Kemar Roach then struck twice in his first over, coming round the wicket to the left-handed Warner, who nicked the paceman's second delivery to slip for 17, Darren Bravo taking the low catch.
And new man Shane Watson lasted only three balls before misjudging and losing his off stump without troubling the scorers.
Ricky Ponting was fortunate to escape a run-out attempt when on nought, Fidel Edwards missing the stumps, and was then dropped by Adrian Barath off spinner Shane Shillingford on four.
A persistent shower forced an early lunch with Cowan on 14 and Ponting eight in a total of 40 for two.
Cowan should have been run out by Baugh shortly after the resumption before a Ponting boundary brought up Australia's half-century.
Roach failed with a hopelessly optimistic review after Ponting was given not out, but a second lbw appeal later in the same over accounted for Cowan, for 20, and with him the first Australian review.
Ponting began to find some fluency and threaded a superb on-drive off Shane Shillingford to the boundary, but he was stopped in his tracks when the rain returned to end the day's play.
Ponting was 32 not out with his successor as captain, Michael Clarke, three not out at the other end and Roach having taken three for 27 and eight wickets in the Test, the best match figures of his career.
Hopes of a result tomorrow will rest on the tourists making quick runs upon the resumption followed by an aggressive declaration from Clarke, but with rain having disrupted the last three days a draw looks the likeliest outcome.