Ben Hilfenhaus put Australia on top with the ball after Ryan Harris sparked a remarkable comeback with the bat in the first Test against the West Indies in Barbados.
At stumps on day four, the Windies were 5-71, leading by 114 runs with five wickets remaining in their second innings.
Peter Siddle (1-11) claimed the vital wicket of Darren Bravo (32) in the closing overs of the day after a 50-run stand between the left-hander and Narsingh Deonarine (20no) to ensure Australia go into the last day's play chasing a win to go 1-0 up in the three-Test series.
The tourists could have reached stumps on even more of a high but Carlton Baugh (2no) survived an LBW appeal which was reviewed by Australia when he padded up to Siddle in the last over of the day.
Australia's position of strength hardly seemed likely midway through Tuesday's opening session, as three quick wickets left the tourists 8-258 in their first innings and staring down the barrel of a 150-run plus deficit.