Having provided the foundation around which the tourists' first day effort of 258 for four was built, Smith started sedately before getting back into stride in the second hour, progressing by another 40 runs in getting to 175 not out.
On the plus side for the West Indies, Jerome Taylor made good use of the second new ball in completing the fourth five-wicket innings haul of his Test career and third on his home ground.
He bowled Shane Watson for 25 offering no shot and then dispensed with Brad Haddin, whose defence was breached after he had raced to 22 off 23 deliveries, improving his figures at the break to an impressive five for 38 off 23 overs.
During the course of his innings Haddin became just the fourth player to compile 3,000 Test runs at number seven in the batting order.
Kemar Roach shrugged off his inconsistent and expensive effort on the first day to claim the wicket of Mitchell Johnson when Darren Bravo held on to the head-high catch at first slip.
Jason Holder then accounted for Mitchell Starc, raising the prospect of the West Indies finishing off the Australian innings before lunch.
But Josh Hazlewood, promoted by one spot in the order after a 97-run last-wicket stand with Adam Voges in the first Test in Dominica a week earlier, survived a second spell from Taylor while Smith accelerated at the expense of Veerasammy Permaul.
Australia won the first Test by nine wickets inside three days in Dominica last week.
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