Bridgetown: West Indies made Australia work hard but the visitors did just enough as they edged WI to win by 3 wickets. Shane Watson top scored with 52 while Deonarine was the highest wicket taker in the 2nd innings.
Ben Hilfenhaus hit the final run with the light fading fast to give the tourists victory after the hosts had fought back to keep the game in the balance.
A half-century from Shane Watson and a rapid 32 from Mike Hussey were the key contributions as the visitors got home in the gloom.
During the morning the West Indies had added 77 more runs to their overnight total of 71-5 to set a relatively tough target of 192.
The hosts hadn't looked like getting anywhere near that when they started the day on 71-5 and promptly lost Narsingh Deonarine lbw to Ryan Harris.
Darren Sammy's big hitting in the first innings had given the West Indies innings but he went for 14 as he played a delivery late and it dropped behind him and was heading towards the wicket.
Sammy's reaction was to kick the ball away but his footballing skills let him down and he only managed to knock the ball against the stumps.
Carlton Baugh was key to the West Indies reaching a competitive total. On 18, he edged a Ben Hilfenhaus delivery straight to first slip. Michael Clarke, who had just taken himself out of that position, crouched down in disbelief.
It wasn't too costly as with the first ball of his next over Hilfenhaus provoked Baugh into chipping straight to Harris at mid-on and the chance was held.
Fidel Edwards was next to go as he holed out to Watson at mid-off off Siddle.
West Indies last pair batted long enough for lunch to be delayed but, having added 19 runs, Kemar Roach got an inside edge off a Harris ball and it crashed into his stumps.
When they came out, the West Indies set defensive fields from the first ball as though a draw was their only hope. Ed Cowan and David Warner found it hard to score.
Warner, perhaps in frustration, tried to run a Darren Sammy ball to third man but instead he got a thin edge through to Baugh.
Watson eventually settled after some narrow escapes and following the tea break both he and Cowan accelerated the scoring in a clear plan of attack.
Sixty-five runs came in the next 14 overs. When Watson found the man on the boundary when he top-edged a sweep off Deonarine. He'd scored 52 and Australia only needed 86 more runs.
It was the first wicket in what proved to be Deonarine's best spell of Test bowling as he used the rough made by the bowlers' footmarks.
A straight-forward pull shot from Cowan went into the hands of mid-wicket and gave Deonarine his second dismissal and it wasn't long before he bowled one to Ricky Ponting that stayed low and got under his bat.
In his next over, two deliveries later, Deonarine had his fourth. Michael Clarke got a leading edge and Deonarine stooped to pick up an easy catch. Australia still required 52 runs to reach their target and were now five down.
He thought he had a five wicket innings when Matthew Wade was given out lbw by umpire Ian Gould but the batsman used the DRS which supported his belief that he'd hit the ball.
With the light fading Hussey and Wade moved the score along as quickly as possible but both fell to Roach. Wade was caught in the deep and Hussey fell with three runs still needed, bowled in the poor light.
He'd hit 32 off 26 balls and took Australia to the verge of victory. A couple of scampered singles from man of the match Harris and Hilfenhaus saw Australia home.
West Indies 449 for 9 dec and 148 (Hilfenhaus 4-27, Harris 3-31)
Australia 406 for 9 dec and 192 for 7 (Watson 52, Deonarine 4-53)
Result Australia beat West Indies by 3 wickets
MOM Ryan Harris (Australia)