Smith, who batted for almost the entire day after entering the fray in the first over, was unconquered on 135 at stumps as Australia advanced to 258 for four at Sabina Park in Kingston.
On a day when West Indies fast bowler Jerome Taylor was superb, Smith weathered the early storm and faced 278 balls while patiently compiling his runs with a variety of shots on both sides of the wicket.
It was the ninth test century for Australia's test captain-elect and his fifth in his last six Tests.
“Early on it wasn't too easy,” the 26-year-old said in a pitchside interview.
“The ball was swinging around a little bit, a bit of seam on it. It was quite hard initially and then it got easier as the day went on.”
Smith said there was no secret to his success, just lots of hard work and patience at the crease.
“For the last 12 months I've been nice and patient and let the bowlers come to me and get in my areas where I want them to bowl and picked them off then. It worked well again today.”
Smith rode his luck after reaching his century. He was dropped at first slip, had an lbw decision overturned on review, and survived a stumping appeal off the last ball of the day.
Puzzlingly, West Indies captain Dinesh Ramdin did not take the new ball, giving Smith and Shane Watson (20 not out) the luxury of facing tame spin bowling for the final 10 overs of the day instead of the fire of Taylor.
The day had started brightly for the West Indies when Taylor sent down six maiden overs in a sizzling morning session and claimed the scalps of Australian openers David Warner (0) and Shaun Marsh (11) with brilliant deliveries.
Taylor finished the day with 3-18 off 15 outstanding overs.
Australia captain Michael Clarke (47) was the third batsman dismissed, although he should have been on his way earlier after being caught on a no-ball when he had scored only three.
Adam Voges, in just his second test, was the only other Australian to lose his wicket, caught behind for 37 off Taylor.
Australia won the first match in the two-Test series last week. – Reuters
Original source: Smith ton gives Aussies the edge