Resuming on 46 for one on the fifth day, West Indies were all out for 191.
They lost skipper Ramnaresh Sarwan and opener Devon Smith early and slumped to 117 for six at lunch with Clark and pace bowler Brett Lee doing the damage.
Denesh Ramdin and Darren Sammy brought some respectability to the West Indies score with a 67 partnership before Ramdin was run out for 36 but by then Australia had the game in the bag.
Clark, who took three wickets in the first innings, finished with figures of five for 32, his best Test performance.
A day filled with hope for an improving West Indies team, who had competed well for the first four days, turned into a familiar story of failure and batting collapse under pressure.
It began miserably for a sparse home crowd when Sarwan tried to push Clark through the on-side, found a leading edge and Andrew Symonds took a brilliant catch at extra cover, tipping the ball up one-handed before grabbing it at the second attempt.
That was a huge breakthrough for the tourists and it was not long before Clark picked up his third victim when opener Smith was trapped leg before for 28 offering no shot to leave West Indies struggling at 60 for three.
Runako Morton’s innings was typical of the West Indian failure to match Australia’s ruthlessness. He hit two successive fours off Lee but was then trapped leg before in the same over by the Australian spearhead.
Dwayne Bravo looked the last hope for an unlikely home revival but he failed to score, falling into a well-set trap.
Australia skipper Ricky Ponting put Mitchell Johnson at short mid-on and Bravo drove a full length Clark delivery straight into his grateful hands.
Clark was able to make the most of the track with his nagging line and awkward bounce proving too much for the home batsmen.
Shivnarine Chanderpaul, who scored a century in the first innings, was next to go and with him went any lingering hope of a fight from the home side.
With a heavily off-side field, Chanderpaul (11) tried to play Lee through mid-wicket but got himself tangled up and merely punched the ball back for a caught and bowled.
Ramdin and Sammy offered the illusion of resistance until Ramdin was run out and, although Daren Powell added 27 with the pressure off, there was never any danger of Australia failing to get off to a winning start to the series.
The second Test will begin in Antigua on Friday.
Scoreboard
AUSTRALIA (1st Innings) 431 (R.T. Ponting 158, A. Symonds 70 not out, B.J. Hodge 67, M.E.K. Hussey 56; F.H. Edwards 5-104).
WEST INDIES (1st Innings) 312 (S. Chanderpaul 118, R.S. Morton 67).
AUSTRALIA (2nd Innings) 167 (A. Symonds 79; D.J. Bravo 4-47).
WEST INDIES (2nd Innings, overnight 46-1):
D.S. Smith lbw b Clark 28
B.A. Parchment c Haddin b Clark 15
R.R. Sarwan c Symonds b Clark 12
R.S. Morton lbw b Lee 9
S. Chanderpaul c and b Lee 11
D.J. Bravo c Johnson b Clark 0
D. Ramdin run out 36
D.J.G. Sammy lbw b Clark 35
D.B.L. Powell c Haddin b MacGill 27
F.H. Edwards not out 9
A.S. Jaggernauth c Jaques b MacGill 0
EXTRAS (B-4, LB-2, NB-3) 9
TOTAL (all out, 67 overs) 191
FALL OF WKTS: 1-22, 2-55, 3-60, 4-74, 5-80, 6-82, 7-149, 8-172, 9-191.
BOWLING: Lee 22-6-81-2 (2nb); Clark 20-8-32-5 (1nb); Johnson 11-3-29-0; MacGill 14-2-43-2.
RESULT: Australia won by 95 runs.
UMPIRES: Aleem Dar (Pakistan) and R.B. Tiffin (Zimbabwe).
TV UMPIRE: N. Malcolm (West Indies).
MATCH REFEREE: R.S. Mahanama (Sri Lanka).
MAN-OF-THE-MATCH: Stuart Clark.
SECOND TEST: St Peter’s (Antigua), May 30-June 3.
THIRD TEST: Bridgetown, June 12-16.
—Reuters