Openers Moeen Ali (46) and Ian Bell (35 not out) took England more than halfway to their target before their opening partnership was broken and James Taylor (25 not out) joined Bell to finish the job inside 23 overs.
West Indies had won the toss and chosen to bat on a muggy, overcast day at the Sydney Cricket Ground but a calamitous start saw them lose Chris Gayle and Darren Bravo for ducks inside the first over.
All rounder Woakes removed them both caught behind and things did not get much better for the islanders with wickets falling at regular intervals through the remainder of their 131-minute innings.
Lendl Simmons provided the only innings of any substance and a reminder of the firepower West Indies can usually rely upon with a lusty six into the second tier of the historic members' stand.
Once he departed caught at cover by James Tredwell at midwicket for 46, though, the writing was on the wall and two overs later Woakes claimed his fifth wicket when Andre Russell holed out for seven to end the innings.
Jason Holder thought he had made an early breakthrough when he had Ali caught at backward point on seven but the batsman was called back when TV replays showed the new West Indies captain had bowled a no-ball.
Reprieved, Ali assumed the heavier workload in the opening partnership and was four runs shy of his half century when he was caught at extra cover off Kemar Roach after hitting nine fours in his 43-ball knock.
Bell and Taylor put together a 50 partnership in 62 balls to take England to the brink of victory and the latter delivered the coup de grace with a four behind square.
England rested James Anderson and Stuart Broad for their penultimate run-out before they begin their quest for a first World Cup title against co-hosts Australia at the Melbourne Cricket Ground (MCG) on Saturday.
West Indies, who won the first two World Cups in 1975 and 1979, open their campaign against Ireland in Nelson, New Zealand next Monday.
(Editing by Amlan Chakraborty)
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