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West Indies enjoyed by far their best day of the second Test on day three but Australia remained firmly in the box seat at the Melbourne Cricket Ground.
Having started day three on 91 for six, the Windies were in danger of being humiliated as they responded to Australia's 551 for three declared. But Darren Bravo (81) and debutant Carlos Brathwaite (59) dug deep to help them recover to 271 all out.
Australia chose not to enforce the follow-on when play resumed after tea and reached 179 for three at the close, a lead of 459 runs.
Carlos Brathwaite had a couple of bits of luck, with James Pattinson twice overstepping while bowling wicket balls, but brought up his half-century in style with an 11-run over off Nathan Lyon.
The 27-year-old Barbados all-rounder smashed a tossed-up delivery down the ground for four from the opening ball of the 62nd over, slog-swept over long-on for six from the third, then brought up his fifty with a comfortable single from the fourth.
Lyon had his revenge soon after, however, when he brought the 90-run seventh-wicket stand to an end by dismissing Brathwaite caught and bowled on the stroke of the lunch break.
Bravo was looking solid at the other end, and registered his 14th Test fifty by cutting Pattinson through the covers for three in the afternoon session. The Trinidadian's patient half-century came off 154 balls, with five fours.
Kemar Roach and Jerome Taylor both stuck around for a while to hold up the hosts. Roach - twice dropped at short leg by Joe Burns - added 22 before being trapped lbw by Pattinson, and Taylor contributed 15 before becoming Lyon's fourth victim when he loosely edged behind to Peter Nevill.
Bravo eventually fell on 81, five minutes before tea, when he sliced a full delivery from Pattinson to Australia captain Steve Smith at gully.
Jomel Warrican finished 11 not out as West Indies were all out for 271 - still 280 runs behind, but a lot better off than they would likely have expected at the start of Monday's play.
Burns - one of four first-innings centurions - did not look at ease from the outset of Australia's second innings, driving at a wide one and surviving a very close lbw call, and was sent on his way for four in the second over when he chased another full delivery from Windies skipper Jason Holder and succeeded only in nicking to Kraigg Brathwaite at second slip.
David Warner - the only Australian top-order batsman not to score a hundred in the first innings - departed cheaply again. The big-hitting left-hander became Carlos Brathwaite's first Test scalp when he nicked a short ball to gully, where Holder held on for a smart catch over his shoulder.
The dismissal brought about exuberant scenes after a tough couple of days for the visitors, with the players falling over themselves to celebrate.
Usman Khawaja (56) and Smith then put on 77 for the third wicket with the number three bringing up his 50 off 56 balls before edging Holder to Denesh Ramdin.
Smith and Mitchell Marsh then guided Australia to the close with the skipper unbeaten on 70 from as many balls.