Michael Clarke's team were set 257 to win after Darren Bravo's 86 helped the West Indies post a respectable 256 for nine in their 50 overs.
Initially it seemed that total may be beyond them as David Warner and Phillip Hughes were quickly dismissed to leave the Australians struggling at four for two.
But opener Watson snatched the momentum back from the West Indies with a superb innings of 135 in just 98 balls as he peppered the boundary with 15 fours and four sixes.
Watson's flamboyant display put Australia firmly on course for victory, with Adam Voges (43) and Mitchell Marsh, who smashed eight fours in his 19-ball 39 not out ensuring there would be no late revival from the Windies.
Australia, who are in Champions Trophy Group A along with England, New Zealand and Sri Lanka, play their second warm-up fixture against India in Cardiff on Tuesday.
After winning the toss and electing to bat, the West Indies lost opener Devon Smith for just seven when he was caught by wicketkeeper Matthew Wade off the bowling of Mitchell Starc.
However, Australia failed to take advantage of that early breakthrough and Bravo combined with Johnson Charles (55) to give the Windies renewed hope.
They put on 65 for the second wicket before Charles fell lbw to Clint Mckay.
Bravo kept the Windies in the hunt, while Mckay finished with figures of three for 45 from 10 overs and Starc took four for 29 off seven overs.
Kemar Roach threatened to derail Australia's chase when he had both Warner and Hughes caught by wicketkeeper Denesh Ramdin.
But Watson's majestic performance and the support of Voges and Marsh saw Australia canter to the finish line with 67 balls to spare.
India beat Sri Lanka
MS Dhoni's team looked up against it when Sri Lanka posted an imposing total of 333 for five after being put into bat.
But Kohli smashed 144 from 120 balls and Karthik blasted 106 not out from only 81 balls to lead India to victory with one over to spare.
India were struggling at 62 for three in the 13th over and then 110 for four in the 21st over before Kohli and Karthik came to the rescue.
Kohli hit 11 fours and three sixes, while Karthik notched up 12 fours and two sixes as he and Dhoni, who scored 18 not out, helped India finish on 337 for five.
India play their second warm-up game against Australia on June 4 in Cardiff before opening their Champions Trophy campaign against South Africa at the same venue two days later.
Ponting scores ton against Surrey
Ricky Ponting, the former Australia captain, marked his English county championship debut for Surrey by compiling an unbeaten 120 against Derbyshire on Saturday.
The 38 year old, who joined up with his new team this week after playing in the Indian Premier League for the Mumbai Indians, struck 13 fours as Surrey reached 362 for four in reply to Derbyshire's first innings 452 all out.
Ponting's experience is a boost for Surrey who are without Graeme Smith, the South Africa captain, due to injury.
Smith was due to captain the county this season but has returned to South Africa for ankle surgery.
Ponting last played county cricket in 2004 for Somerset.
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