With the home side starting the morning in deep trouble at 143 for eight, in reply to the tourists' first innings total of 399, Holder stole the spotlight with a brilliant, counter-attacking innings that lifted them to a final score of 220.
He belted 12 fours and two sixes at Sabina Park, the second taking him to his second Test half-century, off just 63 deliveries and seemed well on course for a second hundred at the highest level of the game.
Roach, who partnered Holder to the middle at the start of play after Veerasammy Permaul was dismissed off the last ball of the second day, played sensibly in a 77-run ninth-wicket partnership with his fellow Barbadian.
He contributed just seven runs but his defiance for 55 minutes, during which he faced 36 deliveries, allowed his fluent partner to enhance his already growing reputation as a batting all-rounder.
Most of his boundaries came from fluent drives and extravagant slashes through the off-side.
Another hundred looked his for the taking until Hazlewood was summoned by Australian captain Michael Clarke for a second spell.
The bowler responded immediately by drawing Roach into edging a drive to wicketkeeper Brad Haddin and then immediately trapping Taylor lbw when the last man offered no shot to his first delivery.
But they survived the examination and were poised, with the rest of a formidable batting line-up to follow, to build on an already impressive lead heading into the afternoon.
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