Brett Lee took 5-5 in 18 blistering balls to breath new life into the second Test in Antigua.
The game looked to be set for a draw, with the West Indies 314-4 in their first innings on the fourth morning.
But helped by some contentious umpiring decisions, Lee ripped through the West Indies batting line up to dismiss the hosts for 352, still 127 behind.
Pushing for a victory that appeared impossible just hours earlier, Australia closed on 244-6, 371 ahead.
Ricky Ponting's side will now have hopes of forcing victory on the fifth day and sealing the three Test series having won the opener in Kingston.
And yet, even taking Australia's ability to conjure unlikely victories seemingly from nowhere into account, the turnaround in the morning session was miraculous.
Resuming on 255-4, Shivnarine Chanderpaul and Dwayne Bravo appeared untroubled as they added 60 comfortable runs against an attack that appeared to be running out of ideas.
And Bravo, who has received some criticism for failing to build on solid starts, appeared to be in the mood for a big score until he was the victim of the first of umpire Russell Tiffin's terrible decisions.
Tiffen raised his finger after Australia's ambitious appeals following a short pitched Lee delivery that clearly flicked Bravo's hip pad rather than bat on its way through to Brad Haddin.
Tiffen was again culpable the very next ball. Lee's inswinging yorker was fast and threatening, but it hit Denesh Ramdin well outside the line of off stump.
Darren Sammy survived the hat-trick ball and Chanderpaul completed his century in the next over, but the controversy soon returned.
606: DEBATE
However, Tiffen's errors should not overshadow a wonderful display of fast bowling by Lee, who claimed Jerome Taylor as his next victim, clean bowling him with a beautiful slower ball.
Two balls later, Daren Powell was the victim of an lbw decision that left no room for complaint.
Mitchell Johnson finished the West Indies innings having Fidel Edwards caught behind, leaving Chanderpaul on 107 and Australia 62 overs to build a commanding lead.
Phil Jaques made 76 before being caught behind by Ramdin off Taylor's bowling, while Mike Hussey and Ponting contributed 40 and 38 respectively. Hussey edged behind from Bravo, while Ponting went leg before to Taylor.
Michael Clarke, who made a century in the first innings, was run out for 10 after being slow to react to Andrew Symond's call and Haddin could only make seven before being trapped lbw by Edwards.
Symonds hit a brisk 43 not out, but there was one final piece of controversy in the day's final over, Lee departing somewhat ironically to another terrible decision - given caught behind from a ball that hit high up his arm.
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