Clark captured a test best five wickets for 32 runs from 20 overs to earn the Man-of-the-Match award, as West Indies, chasing 287 runs to win, were dismissed for 191 in their second innings about 40 minutes before the scheduled tea break on the fifth and final day of the Test at Sabina Park.
Leg-spin bowler Stuart MacGill sealed victory, when he had batting bunny Amit Jaggernauth dubiously caught at forward short leg for a duck - a dismissal which TV replays showed that umpire Russell Tiffin's decision was incorrect.
The victory gave Australia a 1-0 lead in the three-Test series which continues on Friday in Antigua and concludes with the third and final Test in Barbados, starting on June 12.
Denesh Ramdin hit the top score for West Indies in a rearguard effort of 36, Darren Sammy supported him in a 67-run, seventh-wicket stand with 35, opener Devon Smith made 28, and Daren Powell enjoyed himself in a late flourish of 27.
But Clarke made sure the match was over as a genuine contest, when he ripped out Ramnaresh Sarwan and Smith in the first half-hour of the morning to leave the home team 60 for three.
He and Brett Lee shared five wickets in the morning period to bowl Australia into a match-winning position, as West Indies reached 117 for six in their second innings at lunch, following an opening session extended by 30 minutes to compensate for time lost for bad light the previous evening.
In their opening spells, Clark removed Sarwan, Smith, and Dwayne Bravo, and Lee sent back Runako Morton and Shivnarine Chanderpaul to have West Indies reeling on 82 for six.
Clark gave Australia a welcome start, when Sarwan was caught at extra cover for 12 in the third over of the morning to a fine catch from Andrew Symonds.
The West Indies captain was squared-up and was trying a flick at a full length delivery and the ball flew from the leading edge high to left of Symonds, who stretched himself, and contorted his body to allow him to palm the ball up before he quickly turned and clutched the ball with both hands.
Clark's dismissal of Smith was far more straightforward. The left-handed opener was adjudged lbw for 28 in the seventh over of the morning, when he offered no shot to a ball that pitched and straightened.
Lee came close to removing Morton, when the batsman was nearly bowled on one, after he inside-edged a delivery and almost played it into the stumps before he had the presence of mind to kick it away.
But there was no saving Morton, when he drove at a full length delivery from Lee, missed, and was adjudged lbw to Lee for four.
Lee was in the middle of an inspired spell, and had Chanderpaul dropped on five, when the left-hander edged a well-pitched delivery straight into the lap of first slip fielder Simon Katich, and next ball, he had an appeal for an lbw verdict turned down.
But Lee was on the receiving end, when Chanderpaul - who had scored a century in the first innings - responded with a crunching pull through mid-wicket for four.
The Australia strike weapon however, had the last laugh, when he held a return catch to remove Chanderpaul for 11.
Clark piled on the pressure, when he removed Bravo for a duck caught by the short mid-on fielder deliberately positioned for the batsman's penchant to play uppishly through the leg-side.
But Australia could not complete the demolition job before lunch, since Sammy joined Ramdin at the crease, and they batted through the last hour before the interval to stem the fall of wickets.
Wicketkeeper Brad Haddin dropped Ramdin on one off Lee, and short leg fielder Phil Jaques dropped Sammy on four off MacGill, but the Aussies remained on track for victory.
The first half-hour after lunch proved to be one of the less impressive efforts for Australia, as Ramdin and Sammy batted with enterprise, and gathered runs freely off MacGill, in particular, and Mitchell Johnson.
But the breakthrough came once Lee was brought back into the attack, and Ramdin was run out for 26, when he failed to beat MacGill's direct hit at the bowler's end from mid-on going for a single off the Aussie fast bowler.
Jaques on the deep square leg boundary dropped Sammy on 31, when the batsman pulled a short, rising ball from Lee, but Clarke completed his five wicket haul when he had Sammy lbw.
The tailenders - led by Powell - entertained the crowd with some imaginative stroke-play towards the end, but their effort was meaningless.
Australia hold the Frank Worrell Trophy - symbol of Test supremacy against West Indies - and have not lost a Test series in the Caribbean since 1991.