The hosts, overnight 16-2 in pursuit of an improbable target of 392, were all out for only 114 in their second innings, half an hour into the afternoon session on day four at Sabina Park.
Australia's pacers led the way with Mitchell Starc (3-34), Mitchell Johnson (2-23) and Josh Hazlewood (2-18) impressive throughout.
Off-spinner Nathan Lyon wrapped up the match with two wickets in two balls to finish with 2-12.
"We've had to work hard for our wickets but the guys have done that," said Australia captain Michael Clarke. "I'm really happy to win two test matches away from home."
Australia, which won the first of two tests by nine wickets, continued its domination early Sunday. Starc, who picked up both openers for ducks late Saturday, returned to snap up Shane Dowrich, bowled by an inswinging yorker for 4.
Hazlewood then got into the action with two quick wickets to lift his series tally to 12. The big right-armer claimed Darren Bravo (11) to a low edge to gully and then rattled the stumps of a flat-footed Jermaine Blackwood (0).
At 33-5, the West Indies looked in danger of beating its lowest ever test total - 47 against England at this same venue in 2004.
But captain Denesh Ramdin shared a stand of 22 with Shai Hope for the sixth wicket to provide brief resistance.
Hope hit two fours in his 16 before he was undone by a delivery from Mitchell Johnson that snuck through the gate to clatter into the stumps.
Jason Holder could not repeat his first innings heroics and was pouched at midwicket at 62-7 to give all-rounder Shane Watson his first wicket of the series.
Australia could not complete the job before lunch as Ramdin and Permaul put on 49 either side of the break.
Johnson returned to break the stand with his 291st test wicket, drawing him level with bowling coach Craig McDermott as Australia's fifth most prolific wicket-taker at this level.
Ramdin, after compiling 29 off 74 balls, edged to second slip where Clarke took a good, low catch.
The end came swiftly as Lyon ripped through the tail with Kemar Roach (3) giving a bat-pad catch to Steve Smith at short leg and Jerome Taylor missing a huge slog to be bowled first ball.
Smith earned the Man of the Match award for his career-best 199 in Australia's first innings of 399, followed by 54 not out in his team's second innings of 212-2 declared.
West Indies was all out for 220 in its first innings.
"We knew it was going to be tough. We showed some fight but not as long as we wanted to," Ramdin said after the match. "We have to go back to the drawing board, see what we can learn and improve as a team."
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