Off-spinner Nathan Lyon and fast bowler Josh Hazlewood both took three wickets in a balanced Australian attack, while Jermaine Blackwood scored 51 for the home team.
But the day belonged to Australian number three batsman Smith, who fell one run short of his double century when he was adjudged lbw off the bowling of Jerome Taylor after lunch.
The batsman indicated that he got an edge with his bat but, with no hot-spot technology available, the video evidence was inconclusive and the umpire's decision stood.
Smith was only the eighth batsman in test history to be out for 199, and the first since 2008.
He has notched five centuries in his past six tests, and improved his career batting average to more than 55.
Though the 26-year-old narrowly failed to become the third Australian to score a double-century at Sabina Park, it was his highest test score and put his team in a commanding position to sweep the two-test series, after a nine-wicket win last week.
Fast bowler Taylor was easily the pick of the West Indies attack, finishing with career-best figures of 6-47 off 25 impressive overs.
The West Indies fielding was also average. They dropped a couple of catches and a missed stumping did not help the cause.
The home team then plumbed new depths of misery with an inept batting display as the wickets tumbled quickly, notwithstanding the strong Australian attack.
Only Blackwood (51) and Shai Hope (26) made more than 14 runs.
"It was a decent knock but I was a bit disappointed the way I got out," Blackwood told the host broadcaster after dishing up an easy catch to mid-off.
Lyon, meanwhile, was 'very happy' with his figures of 3-35.
"I really enjoyed my time bowling," he said.
"There's enough (in the pitch) if you put the ball in the right area and have patience."
(Reporting by Andrew Both in Cary, North Carolina; editing by Greg Stutchbury)
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