With a first innings lead of 179, the visitors' openers David Warner (62) and Shaun Marsh (69) compiled an opening stand of 117 on the way to individual half-centuries and Steve Smith followed his first innings 199 with an unbeaten 54 yesterday.
Skipper Michael Clarke then determined that, at 212 for two in the final session, the tourists had enough runs on the board and challenged his bowlers to make early inroads in eight testing overs before the close of play.
Both failed to score, Chandrika enduring the indignity of a "pair" on debut, just the second West Indian in the history of Test cricket to have such a chastening experience.
Darren Bravo, who had an lbw verdict off spinner Nathan Lyon overturned on review, will resume on the fourth morning with the inexperienced Shane Dowrich and the odds heavily in Australia's favour to complete victory and a 2-0 series sweep with a day to spare.
With the home side in deep trouble at 143 for eight overnight, Holder stole the spotlight with a brilliant, counter-attacking innings.
He belted 12 fours and two sixes, the second of the towering hits taking him to his second Test half-century, off just 63 deliveries.